Non-Hermitian quantum canonical variables and the generalized ladder operators

Details Non-Hermitian quantum canonical variables and the generalized ladder operators Non-Hermitian quantum canonical variables and the generalized ladder operators

1995-08-07

arxiv.org/abs/hep-th/9508027v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, plain LaTeX

Scientific paper

10.1103/PhysRevA.53.1251

Quantum canonical transformations of the second kind and the non-Hermitian realizations of the basic canonical commutation relations are investigated with a special interest in the generalization of the conventional ladder operators. The operator ordering problem is shown to be resolved when the non-Hermitian realizations for the canonical variables which can not be measured simultaneously with the energy are chosen for the canonical quantizations. Another merit of the non-Hermitian representations is that it naturally allows us to introduce the generalized ladder operators with which one can solve eigenvalue problems quite neatly.

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