Schrödinger and Interaction Pictures

Krishna Thyagarajan

Brian P. Anderson

Alireza R. Baghai-Wadji

This chapter outlines the governing equations in non-relativistic quantum physics. The Schrödinger equation (the Schrödinger picture) looms large. Its intuitive simplicity and elegance render it particularly appealing to aspiring engineers and materials scientists. The other two equivalent pictures presented are the Heisenberg picture and the interaction picture. The Heisenberg picture emphasizes time-dependent operators, and the interaction picture splits the so-called interaction Hamiltonian from the total Hamiltonian of the system considered. Much attention has been paid in this chapter to establish relationships between the pictures, as meaningful as possible at this level of treatment.

JOSIP SEKE

It is shown that if in the projection-operator method an expansion in powers of the interaction Hamiltonian is in view, the usage of the interaction picture is more advantageous than the Schr\"odinger picture. This is also demonstrated in an example.

Kazumoto Ohnami, Kazuya Miyazaki, Y. Mikami

The interaction picture wave packet method is applied to hydrogen scattering with a model Gaussian potential barrier, the linear reaction model. Some new features for the behaviour of the interaction picture wave packet are pointed out. It also splits into two parts according to the separation of the original Schrödinger picture wave packet into transmitted and reflected parts. The interrelation between the two wave packets is discussed in detail. In contrast with the Schrödinger picture wave packet, the reflected part is so clearly defined that we can evaluate the reflection probability as a function of time.

Marianne Breinig