Variational Principle for a Schrödinger Equation with Non-Hermitian Hamiltonian and Position-Dependent Mass

• Autores: Plastino, Angel Ricardo; Vignat, C.; Plastino, A.
• Año de publicación: 2015
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Classical Field Theory; Non-Hermitian Hamiltonian; Position-Dependent Mass; Schrödinger Equation
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

A classical field theory for a Schrödinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro (NR) [Phys. Rev. A 88 (2013) 032105]. This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary field Φ(x,t). It is here shown that the relation between the dynamics of the auxiliary field φ(x,i) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach. Indeed, we formulate a variational principle for the aforementioned Schrödinger equation which is based solely on the wavefunction Ψ(x,t). A continuity equation for an appropriately defined probability density, and the concomitant preservation of the norm, follows from this variational principle via Noether´s theorem. Moreover, the norm-conservation law obtained by NR is reinterpreted as the preservation of the inner product between pairs of solutions of the variable mass Schrödinger equation.
Fil: Plastino, Angel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires; Argentina
Fil: Vignat, C.. University of Tulane; Estados Unidos. Universite D'Orsay; Francia
Fil: Plastino, A.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - la Plata. Instituto de Física la Plata. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Instituto de Física la Plata; Argentina