Eur. Phys. J. D 53, 123-125 (2009)
https://doi.org/10.1140/epjd/e2009-00096-6

Exact solution of N-dimensional radial Schrödinger equation for the fourth-order inverse-power potential

Department of Physics, National Institute of Technology (Technical University), Srinagar 190006, Kashmir, India

Corresponding author: ^a g_r_k_h_a_n@yahoo.co.in

Received: 16 September 2008
Revised: 15 January 2009
Published online: 19 March 2009

Abstract

Radial Schrödinger equation in N-dimensional Hilbert space with the potential V(r)=ar^-1+br^-2+cr^-3+dr^-4 is solved exactly by power series method via a suitable ansatz to the wave function with parameters those also exist in the potential function possibly for the first time. Exact analytical expressions for the energy spectra and potential parameters are obtained in terms of linear combinations of known parameters of radial quantum number n, angular momentum quantum number l, and the spatial dimensions N. Expansion coefficients of the wave function ansatz are generated through the two-term recursion relation for odd/even solutions.