scholarly journals PSEUDOSUPERSYMMETRIC QUANTUM MECHANICS: GENERAL CASE, ORTHOSUPERSYMMETRIES, REDUCIBILITY, AND BOSONIZATION

2003 ◽  
Vol 18 (02) ◽  
pp. 271-292 ◽  
Author(s):  
C. QUESNE ◽  
N. VANSTEENKISTE
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Constant Magnetic Field ◽  
Explicit Solution ◽  
Quantum Mechanical ◽  
Oscillator Algebra ◽  
Quantum Mechanical System ◽  
Irreducible Components ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

Pseudosupersymmetric quantum mechanics (PsSSQM), based upon the use of pseudofermions, was introduced in the context of a new Kemmer equation describing charged vector mesons interacting with an external constant magnetic field. Here we construct the complete explicit solution for its realization in terms of two superpotentials, both equal or unequal. We prove that any orthosupersymmetric quantum mechanical system has a pseudosupersymmetry and give conditions under which a pseudosupersymmetric one may be described by orthosupersymmetries of order two. We propose two new matrix realizations of PsSSQM in terms of the generators of a generalized deformed oscillator algebra (GDOA) and relate them to the cases of equal or unequal superpotentials, respectively. We demonstrate that these matrix realizations are fully reducible and that their irreducible components provide two distinct sets of bosonized operators realizing PsSSQM and corresponding to nonlinear spectra. We relate such results to some previous ones obtained for a GDOA connected with a C3-extended oscillator algebra (where C3 = ℤ3) in the case of linear spectra.

scholarly journals REDUCIBILITY AND BOSONIZATION OF PARASUPERSYMMETRIC AND ORTHOSUPERSYMMETRIC QUANTUM MECHANICS

2002 ◽  
Vol 17 (14) ◽  
pp. 839-849 ◽  
Author(s):  
C. QUESNE ◽  
N. VANSTEENKISTE
Keyword(s):  
Quantum Mechanics ◽  
Fock Space ◽  
Oscillator Algebra ◽  
Irreducible Components ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

Order-p parasupersymmetric and orthosupersymmetric quantum mechanics are shown to be fully reducible when they are realized in terms of the generators of a generalized deformed oscillator algebra and a ℤp+1-grading structure is imposed on the Fock space. The irreducible components provide p + 1 sets of bosonized operators corresponding to both unbroken and broken cases. Such a bosonization is minimal.

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.

EXACT WAVE FUNCTIONS OF MULTI-SPECIES ANYON QUANTUM MECHANICS

1993 ◽  
Vol 08 (29) ◽  
pp. 5101-5113 ◽  
Author(s):  
K.H. CHO ◽  
CHAIHO RIM ◽  
D.S. SOH
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Angular Momentum ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Potential Well ◽  
Quantum Mechanical System ◽  
Ladder Operators ◽  
Free System ◽  
The Many

We investigate the many-anyon quantum-mechanical system of multi-species and obtain algebraically the energy and the angular momentum eigenstates in a harmonic potential well, in a constant magnetic field and of free system using ladder operators. The eigenvalues and their multiplicity of the eigenstates are given.

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 Optimizing adiabaticity in quantum mechanics

2012 ◽  
Vol 90 (2) ◽  
pp. 187-191 ◽  
Author(s):  
R. MacKenzie ◽  
M. Pineault ◽  
L. Renaud-Desjardins
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Mechanical System ◽  
Evolution Operator ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Adiabatic Evolution ◽  
Time Dependent Problem

A condition on the Hamiltonian of an isospectral time-dependent quantum mechanical system is derived, which, if satisfied, implies optimal adiabaticity (defined later). The condition is expressed in terms of the Hamiltonian and the evolution operator related to it. Because the latter depends in a complicated way on the Hamiltonian, it is not yet clear how the condition can be used to extract useful information about the optimal Hamiltonian analytically. The condition is tested on an exactly-soluble time-dependent problem (a spin in a magnetic field), where perfectly adiabatic evolution can be easily identified.

scholarly journals TRANSITION AMPLITUDES WITHIN THE STOCHASTIC QUANTIZATION SCHEME

1994 ◽  
Vol 09 (32) ◽  
pp. 2953-2966 ◽  
Author(s):  
H. HÜFFEL ◽  
H. NAKAZATO
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Constant Magnetic Field ◽  
Quantum Mechanical ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Nonrelativistic Particle ◽  
Mechanical Transition ◽  
Transition Amplitudes

Quantum mechanical transition amplitudes are calculated within the stochastic quantization scheme for the free nonrelativistic particle, the Harmonic oscillator and the nonrelativistic particle in a constant magnetic field; we conclude with free Grassmann quantum mechanics.

scholarly journals Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics

2018 ◽  
Vol 4 (1) ◽  
pp. 47-55
Author(s):  
Timothy Brian Huber
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Mechanical System ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Intertwining Operator

The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.

MAGNETIC GROUP ON THE PSEUDOSPHERE

1992 ◽  
Vol 06 (21) ◽  
pp. 3525-3537 ◽  
Author(s):  
V. BARONE ◽  
V. PENNA ◽  
P. SODANO
Keyword(s):  
Magnetic Field ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Constant Magnetic Field ◽  
Coherent States ◽  
Compact Operators ◽  
Point Of View ◽  
Algebraic Point ◽  
Planar Limit ◽  
Discrete Part

The quantum mechanics of a particle moving on a pseudosphere under the action of a constant magnetic field is studied from an algebraic point of view. The magnetic group on the pseudosphere is SU(1, 1). The Hilbert space for the discrete part of the spectrum is investigated. The eigenstates of the non-compact operators (the hyperbolic magnetic translators) are constructed and shown to be expressible as continuous superpositions of coherent states. The planar limit of both the algebra and the eigenstates is analyzed. Some possible applications are briefly outlined.

FROM RELATIVISTIC VECTOR MESONS IN CONSTANT MAGNETIC FIELDS TO NONRELATIVISTIC (PSEUDO)SUPERSYMMETRIES

1995 ◽  
Vol 10 (19) ◽  
pp. 2783-2797 ◽  
Author(s):  
J. BECKERS ◽  
N. DEBERGH
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Magnetic Fields ◽  
Constant Magnetic Field ◽  
Vector Mesons ◽  
One Dimensional ◽  
Recent Developments

Results coming from the study of relativistic vector mesons interacting with a constant magnetic field are examined through Johnson-Lippmann implications on one-dimensional oscillatorlike systems. We obtain specific nonrelativistic Hamiltonians showing new properties in quantum mechanics and leading to superpositions of bosons and pseudofermions. Moreover, two “potentials” are introduced and discussed in comparison with recent developments usually obtained in p=2 parasupersymmetric quantum mechanics. Pseudofermions are also examined, particularly with respect to orthofermions.

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