Symmetrized exponential oscillator

Abstract

Several properties of bound states in potential $V(x)=g^2\exp (|x|)$ are studied. Firstly, with the emphasis on the reliability of our arbitrary-precision construction, wave functions are considered in the two alternative (viz., asymptotically decreasing or regular) exact Bessel-function forms which obey the asymptotic or matching conditions, respectively. The merits of the resulting complementary transcendental secular equation approaches are compared and their applicability is discussed.

14 pp., 6 figures

References in corpus (15)

• Supersymmetry and Quantum Mechanics
• Schrödinger operators with complex potential but real spectrum
• PT symmetric square well
• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
• Exact solution of the Schrödinger equation for the inverse square root potential $V_0/\sqrt{x}$
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Spontaneous breakdown of PT symmetry in the solvable square-well model
• Coupled-channel version of PT-symmetric square well
• One-dimensional Schrödinger equation with non-analytic potential $V(x)=-g^2\exp (-|x|)$ and its exact Bessel-function solvability
• Morse potential, symmetric Morse potential and bracketed bound-state energies
• Symmetrized quartic polynomial oscillators and their partial exact solvability
• Quantum star-graph analogues of PT-symmetric square wells
• PT-supersymmetric partner of a short-range square well
• Accurate calculation of the complex eigenvalues of the Schrödinger equation with an exponential potential
• Markov constant and quantum instabilities

Cited by in corpus (6)

• Quasi-exactly solvable symmetrized quartic and sextic polynomial oscillators
• A conditionally integrable bi-confluent Heun potential involving inverse square root and centrifugal barrier terms
• Exactly solvable piecewise analytic double well potential $V_D(x)=min[(x+d{)}^2,(x-d{)}^2]$ and its dual single well potential $V_S(x)=max[(x+d{)}^2,(x-d{)}^2]$
• Displaced harmonic oscillator $V\sim \min [(x+d{)}^2,(x-d{)}^2]$ as a benchmark double-well quantum model
• Swanson Hamiltonian: non-PT-symmetry phase
• The third five-parametric hypergeometric quantum-mechanical potential