Bicomplex quantum mechanics. II: The Hilbert space

DOI10.1007/s00006-006-0008-5zbMath1142.81010arXivquant-ph/0510203OpenAlexW2014683741MaRDI QIDQ871880

Sébastien Tremblay, Dominic Rochon

Publication date: 27 March 2007

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0510203

zbMATH Keywords

Hilbert spacesfree moduleslinear functionalsself-adjoint operatorsbicomplex numbershyperbolic numbersgeneralized quantum mechanicscomplex Clifford algebras

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10)

Related Items (34)

\(f\)-algebra structure on hyperbolic numbers ⋮ Topological bicomplex modules ⋮ Multicomplex wave functions for linear and nonlinear Schrödinger equations ⋮ Bicomplex weighted Hardy spaces and bicomplex \(C^*\)-algebras ⋮ Holographic coordinates ⋮ On the quantum mechanics of bicomplex Hamiltonian system ⋮ The complex algebra of physical space: a framework for relativity ⋮ Harmonic morphisms and bicomplex manifolds ⋮ Unnamed Item ⋮ Maximal ideals in a bicomplex algebra and bicomplex Gelfand–Mazur theorem ⋮ Conjugate complex harmonic functions ⋮ Riemann–Liouville fractional operators of bicomplex order and its properties ⋮ Bicomplex modules with indefinite inner product ⋮ On the mean ergodic theorem in bicomplex Banach modules ⋮ Mean value theorems for bicomplex harmonic functions ⋮ Bicomplex harmonic and isotonic oscillators: the excited states ⋮ On a relation of bicomplex pseudoanalytic function theory to the complexified stationary Schrödinger equation ⋮ The Schwarz lemma in bicomplex analysis ⋮ A multicomplex Riemann zeta function ⋮ On holomorphic hypercomplex connections ⋮ On bicomplex Fourier–Wigner transforms ⋮ Some fundamental theorems of functional analysis with bicomplex and hyperbolic scalars ⋮ Finite-dimensional bicomplex Hilbert spaces ⋮ Infinite dimensional bicomplex spectral decomposition theorem ⋮ Bicomplex linear operators on bicomplex Hilbert spaces and Littlewood's subordination theorem ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Bicomplex analogs of Segal-Bargmann and fractional Fourier transforms ⋮ On Factorization of Bicomplex Meromorphic Functions ⋮ Bicomplex Fibonacci quaternions ⋮ On anti-Hermitian metric connections preserving a bicomplex structure ⋮ Algebraic properties of bihyperbolic numbers ⋮ A Comparison of Norms: Bicomplex Root and Ratio Tests and an Extension Theorem ⋮ ON BICOMPLEX-HOLOMORPHIC MANIFOLDS

This page was built for publication: Bicomplex quantum mechanics. II: The Hilbert space