Deriving the Kramers’ dispersion formula from the canonical transformations of Heisenberg’s equation of motion

Abstract

We obtain the canonical transformations for the time-dependent Hamiltonian from Heisenberg’s equation of motion, based on which we derive the Kramers’ dispersion formula via the perturbation theory of matrix mechanics to the second order approximation.

Keywords

• Canonical transformations
• Heisenberg’s equation of motion
• Perturbation theory
• Kramers’ dispersion formula