CoulombF
Regular Coulomb wave function
Calling Sequence
Parameters
Description
Examples
References
CoulombF(L, n, p)
L
-
algebraic expression
n
p
CoulombF is the regular Coulomb wave function. It satisfies the differential equation
y''x+1−2nx−LL+1x2yx=0
CoulombF0,0,x
sinx
CoulombF3,0,x
πxcosxx3−6sinxx2−15cosxx+15sinxπx72
CoulombF2.4,1.7,−3.2+I
0.001110433908
The derivative of the CoulombF function.
diffCoulombFL,n,x,x
L+12x+nCoulombFL,n,xL+1−L+12+n2CoulombFL+1,n,xL+1
Coulomb_ODE≔diffyx,x,x+1−2nx−LL+1x2yx
Coulomb_ODE≔ⅆ2ⅆx2yx+1−2nx−LL+1x2yx
odetestyx=CoulombFL,n,x,Coulomb_ODE
0
dsolveCoulomb_ODE
yx=c__1WhittakerMIn,L+12,2Ix+c__2WhittakerWIn,L+12,2Ix
CoulombFL,n,x=convertCoulombFL,n,x,WhittakerM
CoulombFL,n,x=2LΓ1+L+InxL+1WhittakerMIn,L+12,2Ixⅇnπ2Γ2+2L2IxL+1
Abramowitz, M., and Stegun, I. eds. Handbook of Mathematical Functions. New York: Dover publications.
See Also
convert
dsolve
initialfunctions
odetest
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