Geometrical and physical properties of maths-type q-deformed coherent states for $0 1$
We compare the geometrical and physical properties of the maths-type coherent states for $q>1$ with those of the same for $0 < q < 1$.
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arXiv subjects
V. M. Tkachuk
Publications and source records attributed to V. M. Tkachuk.
Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
In the context of a two-parameter $(α, β)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined by using techniques of supersymmetric quantum mechanics combined with shape invariance under parameter scaling. The resulting supersymmetric partner Hamiltonians correspond to different masses and frequencies. The exponential spectrum is proved to reduce to a previously found quadratic spectrum whenever one of the parameters $α$, $β$ vanishes, in which case shape invariance under parameter translation occurs. In the special case where $α= β\ne 0$, the oscillator Hamiltonian is shown to coincide with that of the q-deformed oscillator with $q > 1$ and its eigenvectors are therefore $n$-$q$-boson states. In the general case where $0 \ne α\ne β\ne 0$, the eigenvectors are constructed as linear combinations of $n$-$q$-boson states by resorting to a Bargmann representation of the latter and to $q$-differential calculus. They are finally expressed in terms of a $q$-exponential and little $q$-Jacobi polynomials.
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Maths-type q-deformed coherent states for q > 1
Maths-type q-deformed coherent states with $q > 1$ allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both position and momentum and are intelligent coherent states for the corresponding deformed Heisenberg algebra.
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Multidimensional quasi-exactly solvable potentials with two known eigenstates
A general approach for constructing multidimensional quasi-exactly solvable (QES) potentials with explicitly known eigenfunctions for two energy levels is proposed. Examples of new QES potentials are presented.
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Factorization and superpotential of the PT symmetric Hamiltonian
We study the factorization of the PT symmetric Hamiltonian. The general expression for the superpotential corresponding to the PT symmetric potential is obtained and explicit examples are presented.
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Supersymmetric approach for generating quasi-exactly solvable potentials with arbitrary two known eigenstates
Using supersymmetric quantum mechanics we construct the quasi-exactly solvable (QES) potentials with arbitrary two known eigenstates. The QES potential and the wave functions of the two energy levels are expressed by some generating function the properties of which determine the state numbers of these levels. Choosing different generating functions we present a few explicit examples of the QES potentials.
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Motion of a spin 1/2 particle in shape invariant scalar and magnetic fields
We study the motion of a spin 1/2 particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics(SUSYQM). We also introduce the concept of shape invariant scalar and magnetic fields and it is shown that the problem admits exact analytical solutions when such fields are considered.
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Supersymmetry of a spin 1/2 particle on the real line
We study one dimensional supersymmetric (SUSY) quantum mechanics of a spin 1/2 particle moving in a rotating magnetic field and scalar potential. We also discuss SUSY breaking and it is shown that SUSY breaking essentially depends on the strength and period of the magnetic field. For a purely rotating magnetic field the eigenvalue problem is solved exactly and two band energy spectrum is found.
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Quasi-Exactly Solvable Potentials with Three Known Eigenstates
We propose a new SUSY method for construction of the quasi-exactly solvable (QES) potentials with three known eigenstates. New QES potentials and corresponding energy levels and wave functions of the ground state and two lowest excited state are obtained. The proposed scheme allows also to construct families of exactly solvable non-singular potentials which are SUSY partners of the well-known ones.
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Quasi-Exactly Solvable Potentials with Two Known Eigenstates
A new supersymmetry method for the generation of the quasi-exactly solvable (QES) potentials with two known eigenstates is proposed. Using this method we obtained new QES potentials for which we found in explicit form the energy levels and wave functions of the ground state and first excited state.
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Supersymmetric Method for Constructing Quasi-Exactly and Conditionally-Exactly Solvable Potentials
Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES). The considered QES potentials at certain values of parameters become exactly solvable and can be treated as CES ones.
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Supersymmetric Method for Constructing Quasi-Exactly Solvable Potentials
We propose a new method for constructing the quasi-exactly solvable (QES) potentials with two known eigenstates using supersymmetric quantum mechanics. General expression for QES potentials with explicitly known energy levels and wave functions of ground state and excited state are obtained. Examples of new QES potentials are considered.
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Supersymmetry of a Nonstationary Pauli Equation
The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra the solutions of nonstationary Pauli equation are generated.
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