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Supersymmetric symplectic quantum mechanics

de Menezes, Miralvo B. ; Fernandes, M.C.B. ; Martins, Maria das Graças R. ; Santana, A.E. ; Vianna, J.D.M.

Annals of physics, 2018-02, Vol.389, p.111-135 [Periódico revisado por pares]

United States: Elsevier Inc

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Título:
Supersymmetric symplectic quantum mechanics
Autor: de Menezes, Miralvo B. ; Fernandes, M.C.B. ; Martins, Maria das Graças R. ; Santana, A.E. ; Vianna, J.D.M.
Assuntos: ALGEBRA ; CALCULATION METHODS ; CHARGED PARTICLES ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; EIGENVALUES ; FACTORIZATION ; Hamiltonian hierarchy ; HAMILTONIANS ; HILBERT SPACE ; MAGNETIC FIELDS ; PHASE SPACE ; QUANTUM MECHANICS ; QUANTUM SYSTEMS ; Quantum theory ; SPECTRA ; SUPERSYMMETRY ; Wigner function
É parte de: Annals of physics, 2018-02, Vol.389, p.111-135
Descrição: Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville–von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.
Editor: United States: Elsevier Inc
Idioma: Inglês

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Supersymmetric symplectic quantum mechanics

de Menezes, Miralvo B. ; Fernandes, M.C.B. ; Martins, Maria das Graças R. ; Santana, A.E. ; Vianna, J.D.M.

United States: Elsevier Inc

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