Alternative approach to the solution of the momentum-space Schrodinger equation for bound states of the N-dimensional Coulomb problem

作者：Szmytkowski Radoslaw^*

来源：Annalen der Physik, 2012, 524(6-7): 345-352.

DOI：10.1002/andp.201100330

• Coulomb problem
• momentum representation
• integral equations
• Gegenbauer polynomials
• Legendre functions

The SchrodingerCoulomb problem in RN, N = 2, is considered in the momentum representation. The adjoint Sturmian eigenvalue problem is discussed first. The resulting radial integral equation is solved with the aid of a symmetric Poisson-type series expansion of the Legendre function of the second kind into products of the Gegenbauer polynomials, established in the 1950's by Ossicini. A relationship between solutions to the Sturmian problem and to an energy eigenvalue problem is then exploited to find the Coulomb bound-state energy levels in RN, together with explicit representations of the associated momentum-space wave functions.

• 出版日期2012-7