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Elias C. Vagenas - One of the best experts on this subject based on the ideXlab platform.
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Generalized uncertainty principle and Self-Adjoint operators
Annals of Physics, 2015Co-Authors: Venkat Balasubramanian, Saurya Das, Elias C. VagenasAbstract:Abstract In this work we explore the Self-Adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are Self-Adjoint or not, or they have Self-Adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the Self-Adjoint extensions of the specific Hamiltonian operator are obtained.
Venkat Balasubramanian - One of the best experts on this subject based on the ideXlab platform.
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Generalized uncertainty principle and Self-Adjoint operators
Annals of Physics, 2015Co-Authors: Venkat Balasubramanian, Saurya Das, Elias C. VagenasAbstract:Abstract In this work we explore the Self-Adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are Self-Adjoint or not, or they have Self-Adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the Self-Adjoint extensions of the specific Hamiltonian operator are obtained.
Evaldo M. F. Curado - One of the best experts on this subject based on the ideXlab platform.
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Position-dependent mass quantum Hamiltonians: general approach and duality
Journal of Physics A, 2016Co-Authors: M. A. Rego-monteiro, Ligia M. C. S. Rodrigues, Evaldo M. F. CuradoAbstract:We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not Self-Adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of Self-Adjoint Hamiltonians which are quantum mechanically equivalent to the non-Self-Adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of Self-Adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrodinger equations generated by the non-Self-Adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual Self-Adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-Self-Adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have Self-Adjoint Hamiltonians that correspond to the non-Self-Adjoint ones found in Harrison's article.
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Position-dependent mass quantum Hamiltonians: General approach and duality
arXiv: Quantum Physics, 2016Co-Authors: M. A. Rego-monteiro, Ligia M. C. S. Rodrigues, Evaldo M. F. CuradoAbstract:We analyze a general family of position-dependent mass quantum Hamiltonians which are not Self-Adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of Self-Adjoint Hamiltonians which are quantum mechanically equivalent to the non Self-Adjoint proposed ones. Inspired in the probability density of the problem, we construct an ansatz for the solutions of the family of Self-Adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrodinger equations generated by the non Self-Adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual Self-Adjoint Hamiltonians. This mapping depends on both the position-dependent mass and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non Self-Adjoint Hamiltonians here studied to a very general family of Hamiltonians proposed in a seminal article of Harrison [1] to describe varying band structures in different types of metals. Therefore, we have Self-Adjoint Hamiltonians that correspond to the non Self-Adjoint ones found in Harrison's article. We analyze three typical cases by choosing a physical position-dependent mass and a deformed harmonic oscillator potential . We completely solve the Schrodinger equations for the three cases; we also find and compare their respective energy levels.
U J Wiese - One of the best experts on this subject based on the ideXlab platform.
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supersymmetric descendants of self adjointly extended quantum mechanical hamiltonians
Annals of Physics, 2013Co-Authors: Munir Alhashimi, M Salman, A Shalaby, U J WieseAbstract:We consider the descendants of Self-Adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of Self-Adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves Self-Adjoint. We also address the Self-Adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general Self-Adjoint extensions is physical. Besides a general characterization of Self-Adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.
Saurya Das - One of the best experts on this subject based on the ideXlab platform.
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Generalized uncertainty principle and Self-Adjoint operators
Annals of Physics, 2015Co-Authors: Venkat Balasubramanian, Saurya Das, Elias C. VagenasAbstract:Abstract In this work we explore the Self-Adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are Self-Adjoint or not, or they have Self-Adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the Self-Adjoint extensions of the specific Hamiltonian operator are obtained.
