Study of anharmonic singular potentials

TL;DR

This paper introduces a variational method to improve eigenenergy calculations for Hamiltonians with singular potentials, providing analytic expressions and optimization techniques to enhance convergence and accuracy.

Contribution

A novel variational approach with closed-form matrix elements and parameter optimization for better eigenenergy computation in singular potential problems.

Findings

Enhanced convergence rates demonstrated

Analytic expressions for matrix elements derived

Comparison shows improved accuracy over previous methods

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.