Hydrogen atom in the momentum representation
The wave functions for the hydrogen atom are determined in the momentum representation, using momentum variables p/sub r/, p/sub theta/, p/sub phi/ which are associated with the spherical polar variables r, t(=e/sup i/..pi.. costheta) and v(=e/sup i/phi). The functions may be written as phi/sub n/,l,m( p/sub r/,p/sub theta/,p/sub phi/) =..cap alpha../sub n/,l( p/sub r/)..beta../sup m//sub l/( p/sub theta/)delta( p/sub phi/+m), ..cap alpha../sub n/,l( p/sub r/)=(n-italic/ip/sub 0/)/sup 3l/+2..sigma../sub k/=0 /sup n/-l-1(/sup n/-l-1k ) (2/sup k/-l+1/(2l+k+1)(2l+k)xxx(l+k+2)) (((ip/sub 0//n)/( p/sub r/-ip/sub 0//n)))/sup l/+k+2, ..beta../sup m//sub l/(p/sub theta/)=..sigma../sub j/=E(m/2) /sup E/(l/2) a/sub j/p/sub theta//sup( -m/+1)/2J/sub j/-(m-1)/2( p/sub theta/), where delta is the Dirac delta function and p/sub 0/=Za/sup -1//sub 0/ (a/sub 0/ is the Bohr radius). J/sub ..nu../( p/sub 0/) are Bessel functions of integer or half-integer order. The radial functions are shown to have poles up to order n+1 at p/sub r/=ip/sub 0//n.
- Research Organization:
- Department of Chemistry, The City College of the City University of New York, New York, New York 10031
- OSTI ID:
- 5190795
- Journal Information:
- Phys. Rev., A; (United States), Journal Name: Phys. Rev., A; (United States) Vol. 22:3; ISSN PLRAA
- Country of Publication:
- United States
- Language:
- English
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