• Quantum motion over a finite one-dimensional domain: With and without dissipation

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      https://www.ias.ac.in/article/fulltext/pram/047/05/0371-0377

    • Keywords

       

      Generalized boundary conditions; free particle; finite domain; dissipation; Schrödinger-Langevin equation

    • Abstract

       

      Quantum motion of a single particle over a finite one-dimensional spatial domain is considered for the generalized four parameter infinity of boundary conditions (GBC) of Carreauet al [1]. The boundary conditions permit complex eigenfunctions with nonzero current for discrete states. Explicit expressions are obtained for the eigenvalues and eigenfunctions. It is shown that these states go over to plane waves in the limit of the spatial domain becoming very large. Dissipation is introduced through Schrödinger-Langevin (SL) equation. The space and time parts of the SL equation are separated and the time part is solved exactly. The space part is converted to nonlinear ordinary differential equation. This is solved perturbatively consistent with the GBC. Various special cases are considered for illustrative purposes.

    • Author Affiliations

       

      Ashok Pimpale1

      1. Inter-University Consortium for Department of Atomic Energy Facilities, University Campus, Khandwa Road, Indore - 452 001, India
    • Dates

       
  • Pramana – Journal of Physics | News

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