• On solving the Schrödinger equation for a complex deictic potential in one dimension

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      https://www.ias.ac.in/article/fulltext/pram/083/03/0301-0316

    • Keywords

       

      Non-Hermitian Hamiltonian; $\mathcal{PT}-symmetry; closed-form solutions.

    • Abstract

       

      Making use of an ansatz for the eigenfunction, we investigate closed-form solutions of the Schrödinger equation for an even power complex deictic potential and its variant in one dimension. For this purpose, extended complex phase-space approach is utilized and nature of the eigenvalue and the corresponding eigenfunction is determined by the analyticity property of the eigenfunction. The imaginary part of the energy eigenvalue exists only if the potential parameters are complex, whereas it reduces to zero for real coupling parameters and the result coincides with those derived from the invariance of Hamiltonian under $\mathcal{PT}$ operations. Thus, a non-Hermitian Hamiltonian possesses real eigenvalue, if it is $\mathcal{PT}$-symmetric.

    • Author Affiliations

       

      Ram Mehar Singh1

      1. Department of Physics, Ch. Devi Lal University, Sirsa 125 055, India
    • Dates

       
  • Pramana – Journal of Physics | News

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