Related papers: Energy Eigenvalues For Supersymmetric Potentials v…
We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two…
The supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian deformed Morse and P\"{o}schl-Teller potentials are obtained by solving the Schr\"{o}dinger equation. The Hamiltonian hierarchy method is used to get the real energy…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
The Hamilton-Jacobi equation on metric spaces has been studied by several authors; following the approach of Gangbo and Swiech, we show that the final value problem for the Hamilton-Jacobi equation has a unique solution even if we add a…
Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
We study SUSY-intertwining for non-Hermitian Hamiltonians with special emphasis to the two-dimensional generalized Morse potential, which does not allow for separation of variables. The complexified methods of SUSY-separation of variables…
We analyze transition potentials $(V(r) \stackrel{r\sim 0}{\rightarrow} {\alpha r^{-2}})$ in non-relativistic quantum mechanics using the techniques of supersymmetry. For the range $-1/4 < \alpha < 3/4$, the eigenvalue problem becomes…
We present the analytic solution for the stationary quantum HamiltonJacobi equation. Knowing the strong relation between the Riccati and quantum Hamilton-Jacobi equations, we develop a simple method to obtain the exact solution. Then, in…
We find theoretical results on energy eigenvalues and corresponding supersymmetric Hamiltonians reflect contradictory behavior for negative values of A. furthermore the resulting supersymmetric partners potentials can be model scattering…
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
Following a letter by Bassett, we show first that it is possible to find an analytical approximation to the error function in terms of a finite series of hyperbolic tangents from the supersymmetric (SUSY) solution of the Poschl-Teller…
New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this…
A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum…
Despite its common use in quantum theory, the mathematical requirement of Dirac Hermiticity of a Hamiltonian is sufficient to guarantee the reality of energy eigenvalues but not necessary. By establishing three theorems, this paper gives…
Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we…
We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Poschl-Teller and Scarf II, all of which reveal a double series of energy levels along with the corresponding superpotential. Inspired by the…
The aim of this work is to show how supersymmetric (SUSY) quantum mechanics can be applied to the Jaynes-Cummings (JC) Hamiltonian of quantum optics. These SUSY transformations connect pairs of Jaynes-Cummings Hamiltonians characterized by…
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In…