Exponential type complex and non-Hermitian potentials within quantum Hamilton–Jacobi formalism

Abstract

PT-/non-PT-symmetric and non-Hermitian deformed Morse and Pöschl-Teller potentials are studied first time by quantum Hamilton-Jacobi approach. Energy eigenvalues and eigenfunctions are obtained by solving quantum Hamilton-Jacobi equation.

The quantum effective mass Hamilton–Jacobi problem

“…A short discussion on the multiplicities G(x) may have the number of poles because of the mass and effective potentials. In the previous works, there were not any comments on the multiplicity of the poles [3,8,9,12]. In terms of the multiplicities of the poles of G(x), the maximum number of distinct meromorphic solutions can be discussed.…”

“…Some detailed and interesting work on extensions of analytical mechanics to the complex plane can be found in [11]. In [12], the spectrum for the class of potentials within QHJ theory is obtained.…”

Exact treatment of the relativistic double ring-shaped Kratzer potential using the quantum Hamilton–Jacobi formalism

“…To obtain a nonrelativistic limit with a potential V and not 2V , 18 one has to scale appropriately the potential terms in Eq. (12). So, one can rewrite the stationary Klein-Gordon equation, under the condition S = V , as:…”

“…5 A relativistic extension was developed and applied by Choi and coworkers to some central potentials in the context of the Klein-Gordon and Dirac equations. 6,7 Also, this method was used to study quasi-exactly solvable models 8 and to obtain analytical solutions for two-dimensional central potentials, 9 for two-dimensional singular oscillator, 10 supersymmetric potentials, 11 non-Hermitian exponential-type potentials, 12 PT symmetric Hamiltonians 13,14 and the position-dependent mass problem. 15 The working methodology of this formalism is mainly based on the knowledge of the singularity structure of the quantum momentum function (QMF) defined as the logarithmic derivative of the wave function.…”

Energy spectra of Hartmann and ring-shaped oscillator potentials using the quantum Hamilton–Jacobi formalism

“…Subsequently a relativistic extension of this approach was proposed by Kim and Choi [14,15] where energy spectra of some relativistic systems have been obtained. The quantum Hamilton-Jacobi formalism (QHJF) was also successfully applied to PT symmetric Hamiltonians and non-hermitian exponential-type potentials [16,17], supersymmetric potentials [18], the position-dependent mass model [19] and two dimensional central potentials [20] and two dimensional singular oscillator [21].…”