Maple Document: New Applications
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en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 26 Jul 2021 02:29:40 GMTMon, 26 Jul 2021 02:29:40 GMTNew applications in the Maple Document categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgMaple Document: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=1337
The hidden SO4 symmetry of the hydrogen atom
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In this worksheet, we derive the SO(4) symmetry of the hydrogen atom and its energy spectrum, without explicitly solving Schrodinger’s equation, using the Maple Physics package. While this problem is well known [4], [5], its solution involves several steps manipulating expressions with tensorial quantum operators, including simplifying them by taking into account a combination of commutator rules and Einstein’s sum rule for repeated indices. Therefore, it is an excellent model to test the current status of Computer Algebra Systems (CAS) concerning this kind of quantum-and-tensor-algebra computations and to showcase the CAS technique. The presentation also shows two alternative patterns of steps that can be used for systematically tackling more complicated symbolic problems of this kind.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="The hidden SO4 symmetry of the hydrogen atom" style="max-width: 25%;" align="left"/>In this worksheet, we derive the SO(4) symmetry of the hydrogen atom and its energy spectrum, without explicitly solving Schrodinger’s equation, using the Maple Physics package. While this problem is well known [4], [5], its solution involves several steps manipulating expressions with tensorial quantum operators, including simplifying them by taking into account a combination of commutator rules and Einstein’s sum rule for repeated indices. Therefore, it is an excellent model to test the current status of Computer Algebra Systems (CAS) concerning this kind of quantum-and-tensor-algebra computations and to showcase the CAS technique. The presentation also shows two alternative patterns of steps that can be used for systematically tackling more complicated symbolic problems of this kind.https://www.maplesoft.com/applications/view.aspx?SID=154764&ref=FeedMon, 17 May 2021 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabScanning Tunneling Microscope Animation(Quantum Mechanical Effect of Tunneling)
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This application has provided animation to give a sense of visualization of scanning tunneling microscope. A scanning tunneling microscope is used for scanning surfaces at the atomic level. In practice, the microscope has a very sharp and well-defined tip, and It can distinguish features smaller than 0.1 nm.<img src="https://www.maplesoft.com/view.aspx?si=154760/Image-STM.jpg" alt="Scanning Tunneling Microscope Animation(Quantum Mechanical Effect of Tunneling)" style="max-width: 25%;" align="left"/>This application has provided animation to give a sense of visualization of scanning tunneling microscope. A scanning tunneling microscope is used for scanning surfaces at the atomic level. In practice, the microscope has a very sharp and well-defined tip, and It can distinguish features smaller than 0.1 nm.https://www.maplesoft.com/applications/view.aspx?SID=154760&ref=FeedMon, 22 Mar 2021 04:00:00 ZBehzad Mohasel Afshari, Admitted Ph.D student, School of Advanced Manufacturing & Mechanical Engineering, University of South AustraliaBehzad Mohasel Afshari, Admitted Ph.D student, School of Advanced Manufacturing & Mechanical Engineering, University of South AustraliaQuantum Physics(Double-slit experiment and Quantum tunnelling)
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We have provided two animations in this application. The first one is for the double-slit experiment and the second one is for quantum tunneling.<img src="https://www.maplesoft.com/view.aspx?si=154759/Image-QP.jpg" alt="Quantum Physics(Double-slit experiment and Quantum tunnelling)" style="max-width: 25%;" align="left"/>We have provided two animations in this application. The first one is for the double-slit experiment and the second one is for quantum tunneling.https://www.maplesoft.com/applications/view.aspx?SID=154759&ref=FeedThu, 18 Mar 2021 04:00:00 ZBehzad Mohasel Afshari, Admitted Ph.D student, School of Advanced Manufacturing & Mechanical Engineering, University of South AustraliaBehzad Mohasel Afshari, Admitted Ph.D student, School of Advanced Manufacturing & Mechanical Engineering, University of South AustraliaComplete Active Space Self-Consistent Field Method
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This project addresses the importance of the CASSCF method and its importance in the description of the dissociation of diatomic molecules.
This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154731/projectImageArturo.png" alt="Complete Active Space Self-Consistent Field Method" style="max-width: 25%;" align="left"/>This project addresses the importance of the CASSCF method and its importance in the description of the dissociation of diatomic molecules.
This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154731&ref=FeedWed, 17 Mar 2021 04:00:00 ZArturo SauzaArturo SauzaDensity functional theory: Comparison of different functionals
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Density functional theory (DFT) is a method to calculate the electronic structure and electronic properties of a system. Theoretically, this should give very accurate results. Yet, in computational sciences, some approximations need to be made due to the limited time and space resources. The exchange-correlation term between electrons is often approximated, with more or less accuracy depending on the functionals. Here, we will compare several functionals on different systems, in order to see which kind of approximation is better for a given system. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154733/mignature.png" alt="Density functional theory: Comparison of different functionals" style="max-width: 25%;" align="left"/>Density functional theory (DFT) is a method to calculate the electronic structure and electronic properties of a system. Theoretically, this should give very accurate results. Yet, in computational sciences, some approximations need to be made due to the limited time and space resources. The exchange-correlation term between electrons is often approximated, with more or less accuracy depending on the functionals. Here, we will compare several functionals on different systems, in order to see which kind of approximation is better for a given system. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154733&ref=FeedWed, 17 Mar 2021 04:00:00 ZFlo SzczepaniakFlo SzczepaniakConical Intersections in Polyatomic Molecules
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Nonadiabatic transitions between electronic excited states play important roles in photochemistry and photophysics of molecular systems. One special kind of nonadiabatic transition is an internal conversion process near a conical intersections. A classic example of ultrafast internal conversion through a conical intersection is the ultrafast relaxation process from S2 to S1 of pyrazine. In this work, we introduce the properties of the conical intersection and a minimal model to describe a system with a conical intersection. By applying the parameters in pyrazine based on literatures, we can construct potential energy surfaces with a conical intersection in pyrazine. By tuning the parameters, we can find how these parameters affect the position of a conical intersection. Also, based on literatures, only a few modes contribute to this process in pyrazine. Thus, based on normal mode analysis, we can see motions of 24 normal modes and see the animation of proposed modes in literature which contribute to the process. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154734/CI_maple.png" alt="Conical Intersections in Polyatomic Molecules" style="max-width: 25%;" align="left"/>Nonadiabatic transitions between electronic excited states play important roles in photochemistry and photophysics of molecular systems. One special kind of nonadiabatic transition is an internal conversion process near a conical intersections. A classic example of ultrafast internal conversion through a conical intersection is the ultrafast relaxation process from S2 to S1 of pyrazine. In this work, we introduce the properties of the conical intersection and a minimal model to describe a system with a conical intersection. By applying the parameters in pyrazine based on literatures, we can construct potential energy surfaces with a conical intersection in pyrazine. By tuning the parameters, we can find how these parameters affect the position of a conical intersection. Also, based on literatures, only a few modes contribute to this process in pyrazine. Thus, based on normal mode analysis, we can see motions of 24 normal modes and see the animation of proposed modes in literature which contribute to the process. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154734&ref=FeedWed, 17 Mar 2021 04:00:00 ZShou-Ting HsiehShou-Ting HsiehCoupled Cluster and Equation-of-Motion Coupled Cluster Theories
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Coupled cluster theory is used to find highly accurate numerical solutions to the Schrodinger equation for ground state systems. For excited state systems, equation-of-motion coupled cluster theory can be used instead. This worksheet will briefly explore coupled cluster and equation-of-motion coupled cluster theories and show some representative results. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154747/CCandE.png" alt="Coupled Cluster and Equation-of-Motion Coupled Cluster Theories" style="max-width: 25%;" align="left"/>Coupled cluster theory is used to find highly accurate numerical solutions to the Schrodinger equation for ground state systems. For excited state systems, equation-of-motion coupled cluster theory can be used instead. This worksheet will briefly explore coupled cluster and equation-of-motion coupled cluster theories and show some representative results. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154747&ref=FeedWed, 17 Mar 2021 04:00:00 ZAnna SchoutenAnna SchoutenQuantum Monte Carlo Methods
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Understanding many-body quantum systems usually means solving the Schrödinger equation of a system of many strongly interacting particles. However, there is no analytical solution for most cases. Therefore, numerical approaches are popular in this area. One kind of the famous methods is quantum Monte Carlo. Two sampling schemes based on the Markov chain Monte Carlo introduced in this project are variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). First, we provide a brief introduction to the important Metropolis-Hastings algorithm, which is of great importance during simulation. Then, we review in detail the basic idea and principles of VMC and DMC. Throughout this project, we discuss the applications of these two methods to the first row elements and show the importance of decent trial function choices.
This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154748/Figure_1.jpg" alt="Quantum Monte Carlo Methods" style="max-width: 25%;" align="left"/>Understanding many-body quantum systems usually means solving the Schrödinger equation of a system of many strongly interacting particles. However, there is no analytical solution for most cases. Therefore, numerical approaches are popular in this area. One kind of the famous methods is quantum Monte Carlo. Two sampling schemes based on the Markov chain Monte Carlo introduced in this project are variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). First, we provide a brief introduction to the important Metropolis-Hastings algorithm, which is of great importance during simulation. Then, we review in detail the basic idea and principles of VMC and DMC. Throughout this project, we discuss the applications of these two methods to the first row elements and show the importance of decent trial function choices.
This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154748&ref=FeedWed, 17 Mar 2021 04:00:00 ZSijia ChenSijia ChenMolecular conductivity
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Molecular conductivity is the ability of a molecule conducting electrons on a single molecular level.While recent advancements on instrumentations enabled direct measurements for molecular conductance, it is also of great significance to predict and understand how the current flows through molecular systems, especially single molecules, which could potentially enhance the understanding their charge transport properties. In this worksheet, we will explore the microscopic origin of molecular conductance and current-constraint two-electron reduced density matrix theory in preparation for modeling the molecular conductance.<img src="https://www.maplesoft.com/view.aspx?si=154749/introfig.jpg" alt="Molecular conductivity" style="max-width: 25%;" align="left"/>Molecular conductivity is the ability of a molecule conducting electrons on a single molecular level.While recent advancements on instrumentations enabled direct measurements for molecular conductance, it is also of great significance to predict and understand how the current flows through molecular systems, especially single molecules, which could potentially enhance the understanding their charge transport properties. In this worksheet, we will explore the microscopic origin of molecular conductance and current-constraint two-electron reduced density matrix theory in preparation for modeling the molecular conductance.https://www.maplesoft.com/applications/view.aspx?SID=154749&ref=FeedWed, 17 Mar 2021 04:00:00 ZCoco LiCoco LiAdiabatic Process in Quantum Mechanics
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Solving the time-dependent Schrodinger equation is essential for understanding the actual response of system to external stimuli. Especially, in the experimental point of view, everything we did during the experiment changes the Hamiltonian, so it is hard to explain the result without understanding the time-dependent Schrodinger equation. Unfortunately, however, there are few time-dependent Schrodinger equations which can be solved exactly and need some approximations to solve the problem. In this worksheet, we will explore another approximation called adiabatic approximation which can be used in large, but slow change of Hamiltonian by using the mathematical approach and demonstration with well-known systems. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154750/figure1.jpg" alt="Adiabatic Process in Quantum Mechanics" style="max-width: 25%;" align="left"/>Solving the time-dependent Schrodinger equation is essential for understanding the actual response of system to external stimuli. Especially, in the experimental point of view, everything we did during the experiment changes the Hamiltonian, so it is hard to explain the result without understanding the time-dependent Schrodinger equation. Unfortunately, however, there are few time-dependent Schrodinger equations which can be solved exactly and need some approximations to solve the problem. In this worksheet, we will explore another approximation called adiabatic approximation which can be used in large, but slow change of Hamiltonian by using the mathematical approach and demonstration with well-known systems. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154750&ref=FeedWed, 17 Mar 2021 04:00:00 ZSeung Yeon LeeSeung Yeon LeeNuclear Magnetic Resonance
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This document provides an overview of the theory and applications of nuclear magnetic resonance. It is intended to educate and inform the reader on why resonance occurs, and how the resonance is used in a useful manner. Signal acquisition and processing is outside the scope of this document. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154751/nmr_photo.jpg" alt="Nuclear Magnetic Resonance" style="max-width: 25%;" align="left"/>This document provides an overview of the theory and applications of nuclear magnetic resonance. It is intended to educate and inform the reader on why resonance occurs, and how the resonance is used in a useful manner. Signal acquisition and processing is outside the scope of this document. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154751&ref=FeedWed, 17 Mar 2021 04:00:00 ZJasper BrownJasper BrownBohmian Mechanics
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Bohmian Mechanics offers a novel view of the quantum world by preserving the definite nature of particles. These quantum particles trace out beautiful trajectories that can offer insights into what is normally a murky and probabilistic interpretation of quantum processes. This worksheet strives to introduce the basics of Bohmian theory, to work through some simple analytical examples, and to walk the reader through a numerical calculation of time dependent quantum mechanics. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154752/Screen_Shot_2021-03-17_at_1.10.14_PM.png" alt="Bohmian Mechanics" style="max-width: 25%;" align="left"/>Bohmian Mechanics offers a novel view of the quantum world by preserving the definite nature of particles. These quantum particles trace out beautiful trajectories that can offer insights into what is normally a murky and probabilistic interpretation of quantum processes. This worksheet strives to introduce the basics of Bohmian theory, to work through some simple analytical examples, and to walk the reader through a numerical calculation of time dependent quantum mechanics. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154752&ref=FeedWed, 17 Mar 2021 04:00:00 ZSamuel WarrenSamuel WarrenDispersion Interactions in Density Functional Theory
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Density functional theory (DFT) is a computational approach used to describe the electronic structure and investigate the electronic properties of many-body systems basic on the Hohenberg-Kohn theorem. One of the limitations of density functional theory approaches is the poor performance in describe dispersion interactions between nonbonded atoms. It becomes a serious problem in the large system as dispersion interactions are cumulative. Here, dispersion interactions in density functional theory are introduced, and this worksheet also provides a simple example, dispersion interactions in the dimer Ar-Ar, for college-level students to work out by themselves.This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154753/maple.png" alt="Dispersion Interactions in Density Functional Theory" style="max-width: 25%;" align="left"/>Density functional theory (DFT) is a computational approach used to describe the electronic structure and investigate the electronic properties of many-body systems basic on the Hohenberg-Kohn theorem. One of the limitations of density functional theory approaches is the poor performance in describe dispersion interactions between nonbonded atoms. It becomes a serious problem in the large system as dispersion interactions are cumulative. Here, dispersion interactions in density functional theory are introduced, and this worksheet also provides a simple example, dispersion interactions in the dimer Ar-Ar, for college-level students to work out by themselves.This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154753&ref=FeedWed, 17 Mar 2021 04:00:00 ZQijie ShenQijie ShenThe effect of functional on simple organic molecules using Density functional theory
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Unlike wave mechanics that solve the Schrodinger equation by approximating wave function, density functional theory (DFT) uses density of electrons, thereby reducing the many body quantum mechanics to a one body problem. The challenge in quantum mechanics then is to find the approximation for true wavefunction, while in DFT, the goal is to find the best approximation of exchange-correlation functional Exc(⍴) that enclose all the unknown parts. However, unlike wave mechanics where there is a clear systematic strategy to improve the approximate wave function, there is no such guideline in DFT. In fact, the quality of DFT calculation depends solely on the accuracy of the chosen exchange-correlation functional. Therefore, it is interesting to compare the performance of various functional like LDA, GGA and hybrid functional with experimental value.
This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154754/f1.png" alt="The effect of functional on simple organic molecules using Density functional theory" style="max-width: 25%;" align="left"/>Unlike wave mechanics that solve the Schrodinger equation by approximating wave function, density functional theory (DFT) uses density of electrons, thereby reducing the many body quantum mechanics to a one body problem. The challenge in quantum mechanics then is to find the approximation for true wavefunction, while in DFT, the goal is to find the best approximation of exchange-correlation functional Exc(⍴) that enclose all the unknown parts. However, unlike wave mechanics where there is a clear systematic strategy to improve the approximate wave function, there is no such guideline in DFT. In fact, the quality of DFT calculation depends solely on the accuracy of the chosen exchange-correlation functional. Therefore, it is interesting to compare the performance of various functional like LDA, GGA and hybrid functional with experimental value.
This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154754&ref=FeedWed, 17 Mar 2021 04:00:00 ZZiqing LinZiqing LinMolecular Conductance and NEGF: From a Semi-Classical Picture to a Quantum Model
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As compared to macroscopic conductivity, where electrons flow through a conducting lattice, molecular conductivity when electrons flow through an individual molecule. The unique conductance effects seen in molecular conductors and their small size makes them ideal for designing smaller and more powerful electronics. In this worksheet, we demonstrate the physical cause behind the non-linear I-V curve of molecular conductors, as well as explain how this curve can be calculated using Non-Equilibrium Green’s Function (NEGF) formalisms and self-consistent calculations. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154756/BDT.jpg" alt="Molecular Conductance and NEGF: From a Semi-Classical Picture to a Quantum Model" style="max-width: 25%;" align="left"/>As compared to macroscopic conductivity, where electrons flow through a conducting lattice, molecular conductivity when electrons flow through an individual molecule. The unique conductance effects seen in molecular conductors and their small size makes them ideal for designing smaller and more powerful electronics. In this worksheet, we demonstrate the physical cause behind the non-linear I-V curve of molecular conductors, as well as explain how this curve can be calculated using Non-Equilibrium Green’s Function (NEGF) formalisms and self-consistent calculations. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154756&ref=FeedWed, 17 Mar 2021 04:00:00 ZAlex HinkleAlex HinkleExchange-Correlation Functionals: GGA vs. Meta-GGA
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Density Functional Theory (DFT) is a widely used electronic structure method due to its balance between computational efficiency and reasonable accuracy. One of the many important choices a user must make when utilizing DFT is that of an appropriate exchange-correlation functional for the system being studied. In this worksheet we will explore the theory underlying two groups of functionals: Generalized Gradient Approximation (GGA) and Meta-Generalized Gradient Approximation (meta-GGA). We will then use two different examples to demonstrate how these functionals perform relative to each other.
This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154757/Screen_Shot_2021-03-17_at_4.33.13_PM.png" alt="Exchange-Correlation Functionals: GGA vs. Meta-GGA" style="max-width: 25%;" align="left"/>Density Functional Theory (DFT) is a widely used electronic structure method due to its balance between computational efficiency and reasonable accuracy. One of the many important choices a user must make when utilizing DFT is that of an appropriate exchange-correlation functional for the system being studied. In this worksheet we will explore the theory underlying two groups of functionals: Generalized Gradient Approximation (GGA) and Meta-Generalized Gradient Approximation (meta-GGA). We will then use two different examples to demonstrate how these functionals perform relative to each other.
This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154757&ref=FeedWed, 17 Mar 2021 04:00:00 ZTeffanie GohTeffanie Goh2D-IR: Background and Introduction to Light-Matter Interaction
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2D IR Spectroscopy is a powerful nonlinear technique that enables the study of excited state dynamics in various systems. Here we will introduce the mathematical background required for a concrete understanding of light-matter interaction. This provides the basis for 2D IR experimental design which is lightly touched in the Applications Section. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154758/maple_image.PNG" alt="2D-IR: Background and Introduction to Light-Matter Interaction" style="max-width: 25%;" align="left"/>2D IR Spectroscopy is a powerful nonlinear technique that enables the study of excited state dynamics in various systems. Here we will introduce the mathematical background required for a concrete understanding of light-matter interaction. This provides the basis for 2D IR experimental design which is lightly touched in the Applications Section. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154758&ref=FeedWed, 17 Mar 2021 04:00:00 ZCaitlin BelloraCaitlin BelloraRelativistic Quantum Mechanics
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This worksheet presents an introduction to relativistic quantum mechanics. It begins with a summary of the principles of special relativity and a discussion of why relativistic effects are relevant to systems of interest in chemistry. The Klein Gordon and Dirac equations are then derived to explore how to incorporate relativity into quantum mechanics. Finally, relativistic and non-relativistic computations are compared to investigate how relativistic effects manifest physically. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154718/Untitled.jpg" alt="Relativistic Quantum Mechanics" style="max-width: 25%;" align="left"/>This worksheet presents an introduction to relativistic quantum mechanics. It begins with a summary of the principles of special relativity and a discussion of why relativistic effects are relevant to systems of interest in chemistry. The Klein Gordon and Dirac equations are then derived to explore how to incorporate relativity into quantum mechanics. Finally, relativistic and non-relativistic computations are compared to investigate how relativistic effects manifest physically. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154718&ref=FeedTue, 16 Mar 2021 04:00:00 ZJoseph SpellbergJoseph SpellbergExistence of the Time Dependent Density Functional Theory
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Density Functional Theory or DFT in short, is one of the most sought-after methods for quantum chemical calculations and for investigating condensed matter systems. Although this does not necessarily mean delivering the most accurate results, it often provides an optimum balance between performance (computing time for some given CPU power) and goodness of results. A lot of physical scientists employ this technique as a tool of theoretical proof-of-principle of some experimental observation. This worksheet endeavours to uphold the power of DFT in investigating time-dependent phenomena i.e. dynamics of quantum systems when not in equilibrium. This worksheet uses the Maple Quantum Chemistry Toolbox.<img src="https://www.maplesoft.com/view.aspx?si=154719/daig.png" alt="Existence of the Time Dependent Density Functional Theory" style="max-width: 25%;" align="left"/>Density Functional Theory or DFT in short, is one of the most sought-after methods for quantum chemical calculations and for investigating condensed matter systems. Although this does not necessarily mean delivering the most accurate results, it often provides an optimum balance between performance (computing time for some given CPU power) and goodness of results. A lot of physical scientists employ this technique as a tool of theoretical proof-of-principle of some experimental observation. This worksheet endeavours to uphold the power of DFT in investigating time-dependent phenomena i.e. dynamics of quantum systems when not in equilibrium. This worksheet uses the Maple Quantum Chemistry Toolbox.https://www.maplesoft.com/applications/view.aspx?SID=154719&ref=FeedTue, 16 Mar 2021 04:00:00 ZIndranil GhoshIndranil GhoshQuantum Optimal Control Theory - A Brief Introduction
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This worksheet briefly introduces basic aspects of Quantum Optimal Control Theory, including notions of controllability and the selection of an appropriate cost functional. The worksheet illustrates these concepts by implementing a simple optimization algorithm for a model quantum system and objective.<img src="https://www.maplesoft.com/view.aspx?si=154717/psi-greek-letter.jpeg" alt="Quantum Optimal Control Theory - A Brief Introduction" style="max-width: 25%;" align="left"/>This worksheet briefly introduces basic aspects of Quantum Optimal Control Theory, including notions of controllability and the selection of an appropriate cost functional. The worksheet illustrates these concepts by implementing a simple optimization algorithm for a model quantum system and objective.https://www.maplesoft.com/applications/view.aspx?SID=154717&ref=FeedMon, 15 Mar 2021 04:00:00 ZJoel GardnerJoel Gardner