arXiv subjects
Publications and source records attributed to T. K. Jana.
We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly constructed for this class of Hamitonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system.
It is shown that the results of ref [1] are consistent.
We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are $η$ pseudo-Hermitian and the metric operator is found explicitly in both the cases.
It is shown that for a class of position dependent mass Schroedinger equation the shape invariance condition is equivalent to a potential symmetry algebra. Explicit realization of such algebras have been obtained for some shape invariant potentials.
We obtain exact solutions of the (1+1) dimensional Klein Gordon equation with linear vector and scalar potentials in the presence of a minimal length. Algebraic approach to the problem has also been studied.