Pinaki Roy

Conditionally Exactly Solvable Potentials: A Supersymmetric Construction Method☆

Abstract We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of one-dimensional potentials are constructed whose corresponding Schrodinger eigenvalue problem can be solved exactly under certain conditions of the potential parameters. Examples of quantum systems on the real line and the half line as well as on some finite interval are studied in detail.

Conditionally exactly solvable potentials and exceptional orthogonal polynomials

It is shown that polynomials associated with solutions of certain conditionally exactly solvable potentials obtained via unbroken as well as broken supersymmetry belong to the category of exceptional orthogonal polynomials. Some properties of such polynomials, e.g., recurrence relation, ladder operators, differential equations, etc., have been obtained.

Conditionally exactly solvable problems and non-linear algebras

Abstract Using ideas of supersymmetric quantum mechanics we construct a class of conditionally exactly solvable potentials which are supersymmetric partners of the linear and radial harmonic oscillator. Furthermore we show that this class of problems possesses some symmetry structures which belong to non-linear algebras.

The non-commutative oscillator, symmetry and the Landau problem

AbstractThe isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative. We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and

Comprehensive analysis of conditionally exactly solvable models

\overline{\Theta}

Quasi-exact solvability of Dirac–Pauli equation and generalized Dirac oscillators

for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem.

'Stringy' Coherent States Inspired By Generalized Uncertainty Principle

We study a quantum mechanical potential introduced previously as a conditionally exactly solvable (CES) model. Besides an analysis following its original introduction in terms of the point canonical transformation, we also present an alternative supersymmetric construction of it. We demonstrate that from the three roots of the implicit cubic equation defining the bound-state energy eigenvalues, there is always only one that leads to a meaningful physical state. Finally we demonstrate that the present CES interaction is, in fact, an exactly solvable Natanzon-class potential.

Information entropy of conditionally exactly solvable potentials

Abstract In this paper we demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the sl (2) symmetry are discussed separately in the spherical, cylindrical, and Cartesian coordinates. Some exactly solvable field configurations are also exhibited.

PT symmetry of a conditionally exactly solvable potential

Abstract Coherent States with Fractional Revival property, that explicitly satisfy the Generalized Uncertainty Principle (GUP), have been constructed in the context of Generalized Harmonic Oscillator. The existence of such states is essential in motivating the GUP based phenomenological results present in the literature which otherwise would be of purely academic interest. The effective phase space is Non-Canonical (or Non-Commutative in popular terminology). Our results have a smooth commutative limit, equivalent to Heisenberg Uncertainty Principle. The Fractional Revival time analysis yields an independent bound on the GUP parameter. Using this and similar bounds obtained here, we derive the largest possible value of the (GUP induced) minimum length scale. Mandel parameter analysis shows that the statistics is Sub-Poissonian. Correspondence Principle is deformed in an interesting way. Our computational scheme is very simple as it requires only first order corrected energy values and undeformed basis states.

Non-linear coherent states associated with conditionally exactly solvable problems

We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki-Birula-Mycielski (BBM) inequality has also been tested for a number of states.We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki–Birula–Mycielski inequality has also been tested for a number of states.