Barnana Roy

A Lie algebraic approach to effective mass Schrödinger equations

We use Lie algebraic techniques to obtain exact solutions of the effective mass Schrodinger equation. In particular we use the su(1,1) algebra, both as a spectrum generating algebra and as a potential algebra, to obtain exact solutions of effective mass Schrodinger equations corresponding to a number of potentials. We also discuss the construction of isospectral Hamiltonians for which both the mass and the potential are different.

Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schrödinger Hamiltonians

Abstract Some exactly solvable potentials in the position dependent mass background are generated whose bound states are given in terms of Laguerre- or Jacobi-type X 1 exceptional orthogonal polynomials. These potentials are shown to be shape invariant and isospectral to the potentials whose bound state solutions involve classical Laguerre or Jacobi polynomials.

New nonlinear coherent states and some of their nonclassical properties

We construct a displacement-operator-type nonlinear coherent state and examine some of its properties. In particular, it is shown that this nonlinear coherent state exhibits nonclassical properties such as squeezing and sub-Poissonian behaviour.We construct a displacement-operator-type nonlinear coherent state and examine some of its properties. In particular, it is shown that this nonlinear coherent state exhibits nonclassical properties such as squeezing and sub-Poissonian behaviour.

A generalized quantum nonlinear oscillator

We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the new exactly solvable potentials possess shape invariance symmetry. The solutions are obtained in terms of classical orthogonal polynomials.

Nonclassical properties of the real and imaginary nonlinear Schrödinger cat states

Abstract The real and imaginary nonlinear Schrodinger cat states are introduced. The oscillatory nature of the photon distribution function resulting from the quantum interferences between the two components is shown and quadrature squeezing and antibunching are observed.

Gazeau–Klauder coherent state for the Morse potential and some of its properties

Abstract Using the Gazeau–Klauder formalism we construct coherent state corresponding to the Morse potential. Some properties of this coherent state have also been examined.

A note on the PT invariant periodic potential V(x)=4cos2x+4iV0sin2x

Abstract It is shown that the PT symmetric Hamiltonian with the periodic potential V ( x ) = 4 cos 2 x + 4 i V 0 sin 2 x can be mapped into a Hermitian Hamiltonian for V 0 0.5 , by a similarity transformation. It is also shown that there exist a second critical point of the potential V ( x ) , apart from the known critical point V 0 = 0.5 , for V 0 c ∼ 0.888437 after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out.

Position dependent mass Schrödinger equation and isospectral potentials: Intertwining operator approach

Here, we have studied first- and second-order intertwining approaches to generate isospectral partner potentials of position dependent (effective) mass Schrodinger equation. The second-order intertwiner is constructed directly by taking it as second-order linear differential operator with position dependent coefficients, and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained, which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to remove bound state(s), and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. ...

Effect of position-dependent mass on dynamical breaking of type B and type X2

We investigate effect of position-dependent mass profiles on dynamical breaking of -fold supersymmetry in several type B and type X2 models. We find that -fold supersymmetry in rational potentials in the constant-mass background is steady against the variation of mass profiles. On the other hand, some physically relevant mass profiles can change the pattern of dynamical -fold supersymmetry breaking in trigonometric, hyperbolic and exponential potentials of both type B and type X2. The latter results open the possibility of detecting experimentally the phase transition of -fold as well as ordinary supersymmetry at a realistic energy scale.

\mathcal {N}

The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau–Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different time scales underlying the quadratic energy spectrum are investigated by the phase analysis of the autocorrelation function.