The Atomic System of Units - Maple Programming Help

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The Atomic System of Units

Description

 • The atomic system is based on a unit of mass, the electron mass (approximately equal to $9.1093897{10}^{-31}$ kilograms), a unit of charge, the electron (approximately equal to $1.60217733{10}^{-19}$ coulombs), a unit of action, the planck (equal to Planck's constant over $2\mathrm{\pi }$), and a unit of electric permittivity written as kappa0 (equal to $\frac{1.{10}^{7}}{{c}^{2}}$ farads per meter, or one statfarad per centimeter, where $c$ is the magnitude of the speed of light).
 • By taking combinations of these four units, one can derive four units corresponding to the base dimensions length, mass, time, and electric current.
 • To facilitate using atomic units, enter the command Units[UseContext](Atomic) so that the second, volt, and tesla refer to the atomic and not SI context.
 • When used in conjunction with the UseSystem command, the atomic system sets the following units for the given dimensions.  All units have context Atomic.

 Dimension Name Unit Name mass electron_mass electric charge electron action planck electric permittivity permittivity length bohr time second force hartree/bohr energy hartree power hartree per second electric current electron per second electric potential volt electric capacitance square electron per hartree electric field strength volt per bohr electric displacement electron per bohr squared electric dipole moment electron bohr electric polarizability electron bohr squared per volt magnetic permeability electron_mass bohr per electron squared magnetic flux volt second magnetic flux density tesla magnetic inductance volt second squared per electron magnetizing force hartree per tesla bohr cubed electric dipole moment hartree per tesla magnetic polarizability hartree per tesla squared

Atomic Base Units

 • All atomic base units have the context Atomic, including the second, where one atomic second is approximately  $2.4188843{10}^{-17}$ SI second.

 Dimension Name Unit Name Unit Symbol length bohr a0 mass electron_mass em time second s electric current electron/second e/s

Atomic Derived Units with Special Names and Symbols

 All units have the context Atomic.

 Dimension Name Unit Name Symbol In Terms of Other Atomic Units action planck h_bar + em*a0^2/s energy hartree E0 em*a0^2/s^2 electric permittivity permittivity kappa0 s^2*e^2/a0^3/em electric potential difference volt V E0/e magnetic flux density tesla T em/s/e

 A plus sign (+) indicates an abbreviation.

Examples

 > $\mathrm{convert}\left(1.0,'\mathrm{units}','\mathrm{bohr}','m'\right)$
 ${5.291772084}{}{{10}}^{{-11}}$ (1)
 > $\mathrm{convert}\left(1.0,'\mathrm{units}','{\mathrm{second}}_{\mathrm{Atomic}}','s'\right)$
 ${2.418884328}{}{{10}}^{{-17}}$ (2)
 > $\mathrm{convert}\left(1.0,'\mathrm{units}','\mathrm{hartree}','J'\right)$
 ${4.359743806}{}{{10}}^{{-18}}$ (3)
 > $\mathrm{convert}\left(1.0,'\mathrm{units}','{\mathrm{volt}}_{\mathrm{Atomic}}','V'\right)$
 ${27.21138344}$ (4)

If infolevel is set to a greater integer (possible settings are 1 through 5), more detailed information about the computation method is displayed.

 > ${\mathrm{infolevel}}_{\mathrm{Units}}≔1:$
 > $\mathrm{convert}\left(3.25721,'\mathrm{system}',\frac{'C'}{{'m'}^{2}},'\mathrm{Atomic}'\right)$
 convert/system:   "converting to the units e/a0^2"
 ${0.05692953990}$ (5)
 > $\mathrm{convert}\left(5.23421{10}^{-10},'\mathrm{system}',\frac{{'C'}^{2}}{'J'},'\mathrm{Atomic}'\right)$
 convert/system:   "converting to the units e^2/E0"
 ${8.889788278}{}{{10}}^{{10}}$ (6)
 > $\mathrm{with}\left(\mathrm{Units}[\mathrm{Standard}]\right):$
 > $\mathrm{Units}[\mathrm{UseSystem}]\left('\mathrm{Atomic}'\right)$
 > $\mathrm{Units}[\mathrm{UseContexts}]\left('\mathrm{Atomic}'\right)$

Notes:

 – To enter a unit in 2-D Math input, select the unit from the appropriate Units palette. If the unit you want is not there, select $\mathrm{unit}$ and then enter the unit.
 – In Maple 2015 and later versions, the double brackets around a unit are not displayed unless you are editing the unit.
 > $2.532⟦\frac{'\mathrm{a0}'}{'s'}⟧$
 ${2.532}{}⟦\frac{{\mathrm{a0}}}{{{s}}_{{\mathrm{contexts:-Atomic}}}}⟧$ (7)
 > $2.532⟦\frac{'\mathrm{a0}'}{'{s}_{\mathrm{SI}}'}⟧$
 ${2.532}{}⟦\frac{{\mathrm{a0}}}{{s}}⟧$ (8)
 > $\mathrm{combine}\left(,'\mathrm{units}'\right)$
 convert/system:   "converting to the units a0/s[second:-contexts:-Atomic]"
 ${6.124615118}{}{{10}}^{{-17}}{}⟦\frac{{\mathrm{a0}}}{{{s}}_{{\mathrm{contexts:-Atomic}}}}⟧$ (9)
 > $5⟦\frac{'\mathrm{em}'{'\mathrm{a0}'}^{2}}{'s'}⟧$
 ${5}{}⟦\frac{{\mathrm{em}}{}{{\mathrm{a0}}}^{{2}}}{{{s}}_{{\mathrm{contexts:-Atomic}}}}⟧$ (10)
 > $\mathrm{convert}\left(,'\mathrm{system}'\right)$
 convert/system:   "converting to the units h_bar"
 ${5}{}⟦{\mathrm{h_bar}}⟧$ (11)
 > $\frac{}{⟦'s'⟧}$
 ${5}{}⟦{\mathrm{E0}}⟧$ (12)
 > $\frac{}{{⟦'\mathrm{a0}'⟧}^{2}}$
 ${5}{}⟦\frac{{\mathrm{em}}}{{{s}}_{{\mathrm{contexts:-Atomic}}}^{{2}}}⟧$ (13)
 > $\mathrm{combine}\left(3.25323⟦'F'⟧,'\mathrm{units}'\right)$
 convert/system:   "converting to the units e^2/E0"
 ${5.525289570}{}{{10}}^{{20}}{}⟦\frac{{{e}}^{{2}}}{{\mathrm{E0}}}⟧$ (14)
 > $\frac{}{⟦'m'⟧}$
 ${2.923857310}{}{{10}}^{{10}}{}⟦{\mathrm{κ0}}⟧$ (15)