Study of anharmonic singular potentials

Abstract

A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix elements of H with respect to the eigenfunctions of a soluble singular problem with two free parameters A and B. The matrix eigenvalues are then optimized with respect to A and B for a given N. Applications, convergence rates, and comparisons with earlier work are discussed in detail.

25 pages

References in corpus (10)

• Exact Solutions to the Schrödinger Equation for the potential $V(r)=a{r}^2+b{r}^{-4}+c{r}^{-6}$ in 2D
• Spiked harmonic oscillators
• Variational analysis for a generalized spiked harmonic oscillator
• Calculation of the spiked harmonic oscillators through a generalized pseudospectral method
• Matrix elements for a generalized spiked harmonic oscillator
• Generalized spiked harmonic oscillator
• Part of the D - dimensional Spiked harmonic oscillator spectra
• Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions
• Bound states for spiked harmonic oscillators and truncated Coulomb potentials
• Energy bounds for a class of singular potentials and some related series

Cited by in corpus (3)

• Spherically confined isotropic harmonic oscillator
• The optimized Rayleigh-Ritz scheme for determining the quantum-mechanical spectrum
• Spiked oscillators: exact solution