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Journal of Shangrao Normal University

The Computation of High Order Approximation Formulae in Non-degenerate Stationary Perturbation Theory

Bo Wu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

By the method of expanding wave function and energy level one by one,we compute the high order approximation formulae in non-degenerate stationary perturbation theory,where the wave function is computed to the second order and the energy leve to the third order.

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Exactly solvable models in quantum mechanics are very rare.However, perturbation theory is a powerful tool to research the complex quantum systems and is widely used in theoretical physics and chemistry.For the particle weakly perturbed by the surrounding environment, its energy eigenstate and eigenvalue are separately calculated up to the first-order and second-order perturbation approximations in the undergraduate textbook of quantum mechanics.Whereas in reality, we have to calculate the high-order perturbation correction terms occasionally.Along the same lines of the low-order perturbation correction terms of energy eigenvalues and eigenstate for stationary state perturbation theory in the non-degenerate case, the third-order and fourth-order perturbation correction terms are strictly attained in this paper.Moreover, it points out the essence of perturbation theory and provides its derivation ideas.Students are no longer afraid of tedious derivation and can derive any-order perturbation correction.These results can serve as an extension and supplement for the quantum mechanics textbooks.Furthermore, it is very helpful for students to deeply understand quantum perturbation theory.