Finite-Dimensional Bicomplex Hilbert Spaces

TL;DR

This paper explores finite-dimensional bicomplex Hilbert spaces, establishing foundational results on matrices, operators, and spectral theory, with applications to quantum mechanics concepts like evolution operators.

Contribution

It provides new theoretical insights into bicomplex Hilbert spaces, including spectral decomposition and operator analysis, relevant to quantum mechanics.

Findings

Spectral decomposition theorem for bicomplex operators

Characterization of self-adjoint operators in bicomplex spaces

Applications to quantum evolution operators

Abstract

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including the spectral decomposition theorem. Applications to concepts relevant to quantum mechanics, like the evolution operator, are pointed out.