Spiked harmonic oscillators
数学物理
2015-06-26 v1 math.MP
摘要
A complete variational treatment is provided for a family of spiked-harmonic oscillator Hamiltonians H = -d^2/dx^2 + B x^2 + lambda/x^alpha, B > 0, lambda > 0, for arbitrary alpha > 0. A compact topological proof is presented that the set S = {psi_n} of known exact solutions for alpha = 2 constitutes an orthonormal basis for the Hilbert space L_2(0, infinity). Closed-form expressions are derived for the matrix elements of H with respect to S. These analytical results, and the inclusion of a further free parameter, facilitate optimized variational estimation of the eigenvalues of H to high accuracy.
引用
@article{arxiv.math-ph/0109014,
title = {Spiked harmonic oscillators},
author = {Richard L. Hall and Nasser Saad and Attila B. von Keviczky},
journal= {arXiv preprint arXiv:math-ph/0109014},
year = {2015}
}
备注
32 pages