Barnana Roy

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Publications (5)0 Total impact

  • Article: Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
    Rajkumar Roychoudhury, Barnana Roy, Partha Pratim Dube
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    ABSTRACT: A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation. A set of deformed creation annihilation operators is introduced whose algebra shows that the transformed Hamiltonian has conformal symmetry. The spectrum is obtained using algebraic technique. The superconformal structure of the system is also worked out in detail. An anomaly related to the spectrum of the Hermitian counterpart of the non-Hermitian Hamiltonian with generalized ladder operators is shown to occur and is discussed in position dependent mass scenario.
    01/2013;
  • Article: Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
    Bikashkali Midya, Barnana Roy
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    ABSTRACT: Using an appropriate change of variable, the Schr\"odinger equation is transformed into a second-order differential equation satisfied by recently discovered Jacobi type $X_m$ exceptional orthogonal polynomials. This facilitates the derivation of infinite families of exactly solvable Hermitian as well as non-Hermitian trigonometric Scarf potentials and finite number of Hermitian and infinite number of non-Hermitian PT-symmetric hyperbolic Scarf potentials. The bound state solutions of all these potentials are associated with the aforesaid exceptional orthogonal polynomials. These infinite families of potentials are shown to be extensions of the conventional trigonometric and hyperbolic Scarf potentials by the addition of some rational terms characterized by the presence of classical Jacobi polynomials. All the members of a particular family of these 'rationally extended polynomial-dependent' potentials have the same energy spectrum and possess translational shape invariant symmetry. The obtained non-Hermitian trigonometric Scarf potentials are shown to be quasi-Hermitian in nature ensuring the reality of the associated energy spectra.
    09/2012;
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    Article: A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
    Bikashkali Midya, Barnana Roy, Rajkumar Roychoudhury
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    ABSTRACT: It is shown that the PT symmetric Hamiltonian with the periodic potential V(x) = 4 cos^2 x + 4 i V_0 sin 2x 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 $V_0^c ~ .888437$ after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out.
    04/2010;
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    Article: Coherent state of the effective mass harmonic oscillator
    Atreyee Biswas, Barnana Roy
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    ABSTRACT: We construct coherent state of the effective mass harmonic oscillator and examine some of its properties. In particular closed form expressions of coherent states for different choices of the mass function are obtained and it is shown that such states are not in general x-p uncertainty states. We also compute the associated Wigner functions. Comment: 18 Pages, 5 Figures. To be published in Mod. Phys. Lett. A
    02/2009;
  • Article: On Solutions of Quantum Eigenvalue Problems: A Supersymmetric Approach
    Barnana Roy, Pinaki Roy, Rajkumar Roychoudhury
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    ABSTRACT: We study solutions of various quantum mechanical eigenvalue problems using the formalism of one dimensional supersymmetric quantum mechanics. The problems studied includes among other problems the non-polynomial oscillator and the doubly anharmonic oscillator potentials. The solutions obtained here are of two types — exact analytical solutions and approximate solutions. The method of obtaining exact solutions have been shown to be general enough to be applied to a large class of potentials. The method of obtaining approximate solutions have been studied in details and their accuracy have been compared with exact numerical results.
    Fortschritte der Physik/Progress of Physics 02/2006; 39(3):211 - 258.
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