Approximate analytical states of a polynomial potential: an example of symmetry restoration

Abstract

An approximate analytical expression for the first two eigenvalues of the Schrodinger equation for the potential V(x) = Ax(4) + Bx(2) is achieved by using the Symanzik scaling symmetry. A kind of symmetry restoration when one of the potential parameters changes conveniently is observed. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.