Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1209.1847

A global, dynamical formulation of quantum confined systems

Nuno Costa Dias, João Nuno Prata

Published Sep 9, 2012• 0 citations
arXivHTMLPDF

Abstract

A brief review of some recent results on the global self-adjoint formulation of systems with boundaries is presented. We specialize to the 1-dimensional case and obtain a dynamical formulation of quantum confinement.
DOI
10.48550/arxiv.1209.1847

Related papers

A global, dynamical formulation of quantum confined systems; pp. 290–293

Nuno Costa Dias, João Nuno Prata

A brief review of some recent results on the global self-adjoint formulation of systems with boundaries is presented. We concentrate on the 1-dimensional case and obtain a dynamical formulation of quantum confinement.

Proceedings of the Estonian Academy of Sciences•Oct 28, 2010•1 citation

The Functional Integrals for Quantum Systems with Boundary Conditions and with Hamiltonians Unbounded from Below

Michel Carreau

•Jan 1, 1991•0 citations

Deformation Quantization of Confined Systems

Nuno Costa Dias, João Nuno Prata

The Weyl-Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation, as well as the dynamical equation does not display the expected solutions. In this paper we review some previous results in the subject and add some new contributions. We reformulate the confined energy eigenvalue equation by adding to the Hamiltonian a new (distributional) boundary potential. The new Hamiltonian is proved to be globally defined and self-adjoint. Moreover, it yields the correct Weyl-Wigner formulation of the confined system.

arXiv:quant-ph/0612022•Dec 4, 2006•2 citations

Boundary Conditions for the Dynamical Equations of Quantum Mechanics

Arno Böhm, Hai Viet Bui, Piotr Kielanowski

Journal of Russian Laser Research•Jan 1, 2014•0 citations

DEFORMATION QUANTIZATION OF CONFINED SYSTEMS

Nuno Costa Dias, João Nuno Prata

The Weyl–Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation as well as the dynamical equation do not display the expected solutions. In this paper, we review some previous results on the subject and add some new contributions. We reformulate the confined energy eigenvalue equation by adding to the Hamiltonian a new (distributional) boundary potential. The new Hamiltonian is proved to be globally defined and self-adjoint. Moreover, it yields the correct Weyl–Wigner formulation of the confined system.

International Journal of Quantum Information•Feb 1, 2007•4 citations

Constructing quantum observables and self-adjoint extensions of symmetric operators. III. Self-adjoint boundary conditions

Boris Leonidovich Voronov, Dmitri M Gitman, Igor Viktorovich Tyutin

Russian Physics Journal•Feb 1, 2008•13 citations
The Weyl-Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation, as well as the dynamical equation does not display the expected solutions. In this paper we review some previous results in the subject and add some new contributions. We reformulate the confined energy eigenvalue equation by adding to the Hamiltonian a new (distributional) boundary potential. The new Hamiltonian is proved to be globally defined and self-adjoint. Moreover, it yields the correct Weyl-Wigner formulation of the confined system.
The Weyl–Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation as well as the dynamical equation do not display the expected solutions. In this paper, we review some previous results on the subject and add some new contributions. We reformulate the confined energy eigenvalue equation by adding to the Hamiltonian a new (distributional) boundary potential. The new Hamiltonian is proved to be globally defined and self-adjoint. Moreover, it yields the correct Weyl–Wigner formulation of the confined system.