scholarly journals Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass

2021 ◽  
Vol 62 (9) ◽  
pp. 092101
Author(s):  
Bruno G. da Costa ◽  
Genilson A. C. da Silva ◽  
Ignacio S. Gomez
Keyword(s):  
Quantum Mechanics ◽  
Effective Mass ◽  
Coherent States ◽  
Supersymmetric Quantum Mechanics ◽  
Deformed Oscillator

SUSY coherent states and enhanced canonical quantizations for Pauli model

2021 ◽  
pp. 2150105
Author(s):  
Jean Vignon Hounguevou ◽  
Daniel Sabi Takou ◽  
Gabriel Y. H. Avossevou
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coherent States ◽  
Differential Operators ◽  
Canonical Quantization ◽  
Point Of View ◽  
Supersymmetric Quantum Mechanics ◽  
Geometric Properties

In this paper, we study coherent states for a quantum Pauli model through supersymmetric quantum mechanics (SUSYQM) method. From the point of view of canonical quantization, the construction of these coherent states is based on the very important differential operators in SUSYQM call factorization operators. The connection between classical and quantum theory is given by using the geometric properties of these states.

scholarly journals Susy for Non-Hermitian Hamiltonians, with a View to Coherent States

2020 ◽  
Vol 23 (3) ◽  
Author(s):  
F. Bagarello
Keyword(s):  
Quantum Mechanics ◽  
Physical System ◽  
Coherent States ◽  
Supersymmetric Quantum Mechanics ◽  
Extended Version ◽  
Black Scholes

Abstract We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different, superpotentials. Bi-coherent states of the Gazeau-Klauder type are constructed and their properties are analyzed. Some examples are also discussed, including an application to the Black-Scholes equation, one of the most important equations in Finance.

scholarly journals Minimal bosonization of double-graded quantum mechanics

2021 ◽  
Vol 36 (33) ◽  
Author(s):  
C. Quesne
Keyword(s):  
Quantum Mechanics ◽  
Central Element ◽  
Degree Of Freedom ◽  
Supersymmetric Quantum Mechanics ◽  
Oscillator Algebra ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

The superalgebra of [Formula: see text]-graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. Such an approach is directly inspired by a description of the corresponding [Formula: see text]-graded superalgebra in the framework of a Calogero–Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the [Formula: see text]-graded superalgebra, the central element [Formula: see text] has the property of distinguishing between degenerate eigenstates of the Hamiltonian.

scholarly journals FRACTIONAL SUPERSYMMETRIC QUANTUM MECHANICS, TOPOLOGICAL INVARIANTS AND GENERALIZED DEFORMED OSCILLATOR ALGEBRAS

2003 ◽  
Vol 18 (07) ◽  
pp. 515-525 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Quantum Mechanics ◽  
Fock Space ◽  
Supersymmetric Quantum Mechanics ◽  
Topological Invariants ◽  
Oscillator Algebra ◽  
Irreducible Components ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra ◽  
Witten Index

Fractional supersymmetric quantum mechanics of order λ is realized in terms of the generators of a generalized deformed oscillator algebra and a ℤλ-grading structure is imposed on the Fock space of the latter. This realization is shown to be fully reducible with the irreducible components providing λ sets of minimally bosonized operators corresponding to both unbroken and broken cases. It also furnishes some examples of ℤλ-graded uniform topological symmetry of type (1, 1, …, 1) with topological invariants generalizing the Witten index.

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