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A new algebraic approach to perturbation theory. (English) Zbl 1075.81534
Summary: An algebraic nonperturbative 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 formulas 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).
MSC:
81T15Perturbative methods of renormalization (quantum theory)
81R12Relations of groups and algebras in quantum theory with integrable systems
Software:
Mathematica