Bicomplex Hamiltonian systems in Quantum Mechanics

TL;DR

This paper explores bicomplex Hamiltonian systems within a modified Schrödinger framework, revealing unique PT symmetries and their applications to various oscillators, expanding understanding of quantum systems with bicomplex numbers.

Contribution

It introduces a novel approach to bicomplex Hamiltonian systems, analyzing multiple PT symmetries and their implications in quantum mechanics.

Findings

Identification of three conjugates defining distinct PT symmetries.

Discovery of two compatible PT-symmetric models with unique properties.

Application to harmonic and inverted oscillators revealing new symmetry features.

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.