On the calculation of bound-state energies supported by hyperbolic double well potentials

Relativistic Energies and Scattering Phase Shifts for the Fermionic Particles Scattered by Hyperbolical potential with the Pseudo (Spin) Symmetry

In this paper, we studied the approximate scattering state solutions of the Dirac equation with the hyperbolical potential with pseudospin and spin symmetries. Using a suitable short range approximation within the formalism of functional analytical method, we obtained the spin-orbit quantum numbers dependent scattering phase shifts for the spin and pseudospin symmetries. The normalization constants, lower and upper radial spinor for the two symmetries and the relativistic energy spectra were presented. Our results reveal that both the symmetry constants (C_ps and C_s) and the spin-orbit quantu…

紧支撑抛物线和兰道屏障的精确解

Exact Solutions for Compactly Supported Parabolic and Landau Quantum Barriers

本文推导了紧支撑抛物线和兰道势垒的精确解，给出了透射和反射系数，并计算了相关驻留时间。

Quasi-exact solution to the Dirac equation for the hyperbolic secant potential

We analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that bound states of both positive and negative energies exist in the energy spectrum and that there is a threshold value of the characteristic potential strength for which the first mode appears. Analytical solutions are presented in several limited cases and supercriticality is discussed.

PT-symmetric non-polynomial oscillators and hyperbolic potential with two known real eigenvalues in a SUSY framework

Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials with two known real eigenvalues (the ground state and first-excited state energies). We construct examples, namely those of complexified non-polynomial oscillators and of a complexified hyperbolic potential, to demonstrate how our scheme works in practice. For the former we provide a connection with the sl(2) method, illustrating the comparative advantages of the supersymmetric one.