A New Algebraic Approach to Perturbation Theory

Details A New Algebraic Approach to Perturbation Theory A New Algebraic Approach to Perturbation Theory

2004-12-21

arxiv.org/abs/quant-ph/0412162v2

Mod. Phys. Lett. A 20 (2005) 1683

Physics

Quantum Physics

Scientific paper

10.1142/S0217732305016737

An algebraic non-perturbative approach is proposed for the analytical treatment of Schr\"{o}dinger 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).

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