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Journal of Education Reform and Innovation
(JOERAI)
Face
Volume 1, No.4, 2023
Print version
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DOI:
https://doi.org/10.61957/joerai-20230311 |
Title:
High-order Corrections of Time-independent
Non-degenerate Perturbation Theory |
Author:
Haifeng Li, Kaifeng Zhang, Zhimin Ou and Xiaoguang He |
Abstract |
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.
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Keywords:
Stationary state; Perturbation theory; Energy
Eigenvalues; Eigenstate |
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