Stationary Flows of the Parabolic Potential Barrier in Two Dimensions

Abstract

In the two-dimensional isotropic parabolic potential barrier $V(x,y)=V_0-m{\gamma }^2(x^2+y^2)/2$, though it is a model of an unstable system in quantum mechanics, we can obtain the stationary states corresponding to the real energy eigenvalue $V_0$. Further, they are infinitely degenerate. For the first few eigenstates, we will find the stationary flows round a right angle that are expressed by the complex velocity potentials $W=\pm \gamma z^2/2$.

12 pages, AmS-LaTeX, 4 figures

References in corpus (5)

• Motion of vortex lines in quantum mechanics
• Operator Methods of the Parabolic Potential Barrier
• Entropy Burst from Parabolic Potentials
• Statistical Mechanics for States with Complex Eigenvalues and Quasi-stable Semiclassical Systems
• Complex Eigenvalues of the Parabolic Potential Barrier and Gel'fand Triplet

Cited by in corpus (9)

• Vortices and chirality of magnetostatic modes in quasi-2D ferrite disk particles
• Zero Energy Solutions and Vortices in Schroedinger Equations
• Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers
• Supersymmetric Quantum Mechanics of Scattering
• Modular Schrödinger equation and dynamical duality
• On the upper bound of the electronic kinetic energy in terms of density functionals
• Entropy Burst from Parabolic Potentials
• Zero-Energy Flows and Vortex Patterns in Quantum Mechanics
• "Velocities" in Quantum Mechanics