Roger Balian
Matrix elements of Bogolubov canonical transformations
Evelyn Aronson, I.A. Malkin, Vladimir I. Man’ko
Evaluation of the Bloch density matrix for a charged oscillator in a magnetic field by canonical transformations
Mohammed A. Z. Habeeb
The problem of a charged particle moving in an anisotropic harmonic oscillator potential in the presence of a constant external magnetic field is reduced to that of a particle in an anisotropic oscillator by using canonical transformations. The Bloch density matrix for the original problem is then exactly evaluated by transforming the well known result for the anisotropic oscillator with the aid of the integral kernel corresponding to the canonical transformation under consideration.
Linear Canonical Transformations
Structure of a linear canonical transformation
Alexander V. Shapovalov, V. N. Shapovalov
The Perturbation Theory of Matrix Mechanics Based on its Canonical Transformations
Yong-Yi Huang
We elucidate that the canonical transformations of matrix mechanics are just the transformations of different representations of the standard quantum mechanics, reproduce the non-degenerate, degenerate and time-dependent perturbation theory in three men’s paper, we solve the mystery of time-dependent perturbation theory of matrix mechanics. The Kramers’ dispersion formula from time-dependent perturbation theory of matrix mechanics is also derived from that of wave mechanics.
Standard r-Transformation Matrices and Their Applications
U. Fano, A. R. P. Rau