A new method for the solution of the Schrodinger equation

Abstract

We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wave function and, finally, a short distance scale, in which the wave function is sizable. The key feature of our method is the introduction of an arbitrary parameter in the last two scales, which is then used to optimize a perturbative expansion in a suitable parameter. We apply the method to the quantum anharmonic oscillator and find excellent results.

4 pages, 4 figures, RevTex4

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Cited by in corpus (8)

• Perturbation theory in a framework of iteration methods
• Improved Lindstedt-Poincare method for the solution of nonlinear problems
• Analytical solutions of the Schrödinger equation with the Woods-Saxon potential for arbitrary $l$ state
• Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators
• Quantum anharmonic oscillators: a new approach
• Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential
• Comparative study of quantum anharmonic potentials
• The bound state solutions of the $D$-dimensional Schrödinger equation for the Woods-Saxon potential