Ground-state energy of singular potentials

Abstract

It is shown that for singular potentials of the form λ/rα, the asymptotic form of the wave function both at r→ and r→0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential λ/r4, it is shown that it gives the exact ground-state energy for this potential when λ→0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter λ, a trial basis set of wave functions which also satisfy the correct boundary conditions at r→ ande r→0 are used to find the ground-state energy of the singular potential λ/r4. It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of λ values. © 1994 The American Physical Society.