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Bicomplex Hamiltonian systems in Quantum Mechanics

By Bijan Bagchi and Abhijit Banerjee

Abstract

We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural way, a separate class of time reversal operator. However, the induced parity (P)-time (T)-symmetric models turn out to be mutually incompatible except for two of them which could be chosen uniquely. The latter models are then explored by working within an extended phase space. Applications to the problems of harmonic oscillator, inverted oscillator and isotonic oscillator are considered and many new interesting properties are uncovered for the new types of PT symmetries.Comment: 35 Pages, Revised version, Accepted for publication in Journal of Physics A:Mathematical and Theoritica

Topics: Mathematical Physics, Quantum Physics
Publisher: 'IOP Publishing'
Year: 2015
DOI identifier: 10.1088/1751-8113/48/50/505201
OAI identifier: oai:arXiv.org:1503.04603

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