Perturbations to Energy Levels

Stig Stenholm

Wei Ming

According to the way of the second level amendment of the energy and the wave function in the non-degenerate perturbation theory,the second level amendment of the energy and the wave function are induced in degenerate perturbation theory, which forms the formula of the second level amendment.

Xuehua Jiang

Relativistic effect taken into consideration and a certain quantum resonator energy level being corrected by perturbation theory, the energy level structural formula which is the same as the result obtained by using perturbation items is obtained, but this method is more easier, which offers a new correction for analyzing the energy level of some quantum resonator.

Dale M. Grimes

W.J. Caspers

Amnon Yariv, W. H. Louisell

The subject of transition probabilities induced by random perturbations is treated. The expression for average transition rates between two energy levels is derived for the general case when the frequency spectrum of the perturbation and the distribution of the energy levels have comparable widths. The general expression takes an especially simple form for the special cases where the frequency bandwidth of the perturbation Hamiltonian is either much larger or much smaller than that of the energy level distribution. The formulas are applied, by way of illustration, to a number of physical problems.