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Journal of Mathematical Physics

Lower bounds for quartic anharmonic and double-well potentials

B. L. Burrows, M. Cohen, Tova Feldmann

Published Jan 1, 1993• 289 citations
Publisher

Abstract

Rigorous and remarkably accurate lower bounds to the lower eigenvalue spectrum of the Schrödinger equation with quartic anharmonic and symmetric double-well potentials of the form V(A,B)=Ax2/2+Bx4(B≥0) are presented. This procedure exploits some exactly soluble model potentials and appears to be of quite general utility.
DOI
10.1063/1.530375

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The goal of the dissertation is to find new method of solving two-dimensional Schrödinger equation in such cases, when the separation of the variables is not applicable. The results are applied to the two-dimensional Schrödinger equation with the potentials of the form of the quartic polynomial, of the sextic polynomial and of the quartic Morse potential. For these cases, the analytical formulae for the ground state wave functions and the corresponding energies have been found. For the specific class of the potentials of the form of the quartic polynomial, analytical formula for one of the excited states and for the corresponding energy have been found.
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