Finite-Dimensional Bicomplex Hilbert Spaces

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.

21 pages

References in corpus (2)

• Bicomplex quantum mechanics: I. The generalized Schrödinger equation
• Bicomplex Quantum Mechanics: II. The Hilbert Space

Cited by in corpus (5)

• Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates
• The bicomplex quantum Coulomb potential problem
• Multicomplex Ideals, Modules and Hilbert Spaces
• Determinant, Characteristic Polynomial, and Inverse in Commutative Analogues of Clifford Algebras
• On Commutative Analogues of Clifford Algebras and Their Decompositions