Non-hermitian techniques of canonical transformations in quantum mechanics

Abstract

The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic oscillator is solved in two different types of canonical transformations. The quantum form of the classical Hamiton-Jacobi theory is also employed to solve time dependent Schrödinger wave equations, showing that when one uses the classical action as a generating function of the quantum canonical transformation of time evolutions of state vectors, the corresponding propagator can easily be obtained.

23 pages, LaTeX, CbNU-Th-94-27

References in corpus (2)

• Currents, Charges, and Canonical Structure of Pseudodual Chiral Models
• Quantum Canonical Transformations: Physical Equivalence of Quantum Theories

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• Non-Hermitian quantum canonical variables and the generalized ladder operators
• Controlling Excitations Inversion of a Cooper Pair Box Interacting with a Nanomechanical Resonator
• Implications of invariance of the Hamiltonian under canonical transformations in phase space
• Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics