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CoulombF

Regular Coulomb wave function

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

CoulombF(L, n, p)

Parameters

L

-

algebraic expression

n

-

algebraic expression

p

-

algebraic expression

Description

• 

CoulombF is the regular Coulomb wave function. It satisfies the differential equation

y''x+12nxLL+1x2yx=0

Examples

CoulombF0,0,x

sinx

(1)

CoulombF3,0,x

πxcosxx36sinxx215cosxx+15sinxπx7/2

(2)

CoulombF2.4,1.7,3.2+I

0.001110433908

(3)

The derivative of the CoulombF function.

xCoulombFL,n,x

L+12x+nCoulombFL,n,xL+1L+12+n2CoulombFL+1,n,xL+1

(4)

Coulomb_ODEⅆ2ⅆx2yx+12nxLL+1x2yx

Coulomb_ODE:=ⅆ2ⅆx2yx+12nxLL+1x2yx

(5)

odetestyx=CoulombFL,n,x,Coulomb_ODE

0

(6)

dsolveCoulomb_ODE

yx=_C1WhittakerMIn,L+12,2Ix+_C2WhittakerWIn,L+12,2Ix

(7)

CoulombFL,n,x=convertCoulombFL,n,x,WhittakerM

CoulombFL,n,x=2LΓ1+L+InxL+1WhittakerMIn,L+12,2Ixⅇ12nπΓ2+2L2IxL+1

(8)

References

  

Abramowitz, M., and Stegun, I. eds. Handbook of Mathematical Functions. New York: Dover publications.

See Also

convert

dsolve

initialfunctions

odetest

 


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