2006/10/30 by A. Ganguly, A Ganguly, M. V. Ioffe +3 · 1 citation
Mathematics · Physics and Astronomy · #Bound state #Bounded function #Gas Dynamics and Kinetic Theory #Hamiltonian (control theory) #Operator (biology) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Schrödinger's cat #Spectral Theory in Mathematical Physics #Upper and lower bounds #Wave function #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/47/010
published as J.Phys. A39 (2006) 14659-14680 · To be published in J.Phys.A (Present e-mail of AG: [email protected])
arxiv created 2006/10/30 · openalex publication_date 2006/11/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant. Starting from a generalized effective mass kinetic energy operator the matching and boundary conditions for the envelope wavefunctions are derived. It is shown that in a mapping to an auxiliary constant-mass Schrödinger picture one obtains one-period 'associated Lamé' well bounded by two δ-wells or δ-barriers depending on the values of the ordering parameter β. The results for bound states of this new solvable model are provided for a wide variation of the parameters.