A New Algebraic Approach to Perturbation Theory

Abstract

An algebraic non-perturbative approach is proposed for the analytical treatment of Schrödinger equations with a potential that can be expressed in terms of an exactly solvable piece with an additional potential. Avoiding disadvantages of standard approaches, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an illustration the procedure, well adapted to the use of computer algebra, is successfully applied to quartic anharmonic oscillators by means of very simple algebraic manipulations. The trend of the exact values of the energies is rather well reproduced for a large range of values of the coupling constant (g=0.001-10000).

References in corpus (4)

• Supersymmetry and Quantum Mechanics
• The quantum anharmonic oscillator in the Heisenberg picture and multiple scale techniques
• Supersymmetric quantum mechanics based on higher excited states
• Semiclassical treatment of logarithmic perturbation theory

Cited by in corpus (7)

• An Alternative Treatment for Yukawa-Type Potentials
• A perturbative treatment for the energy levels of neutral atoms
• Remarks on exact solvability of quantum systems with spatially varying effective mass
• Explicit Solutions for N-Dimensional Schrodinger Equations with Position-Dependent Mass
• An extended scenario for the Schrodinger equation
• Equivalence of two alternative approaches to Schrodinger equations
• Application of the asymptotic Taylor expansion method to bistable potentials