Related papers: On susy periodicity defects of the Lame Potentials
Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…
Complex potentials are constructed as Darboux-deformations of short range, radial nonsingular potentials. They behave as optical devices which both refracts and absorbs light waves. The deformation preserves the initial spectrum of energies…
We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its…
The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…
It is shown by analyzing the $1D$ Schr\"odinger equation that discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those discontinuities, which are present in the energies {\it…
Supersymmetry (SUSY) proposed as an elementary symmetry for physics beyond the Standard Model has found important applications in various areas outside high-energy physics. Here, we systematically implement supersymmetric quantum mechanics…
This work is aimed at demonstrating the possibility to construct new exactly-solvable stochastic systems by use of the extended supersymmetric quantum mechanics ($N=4 SUSY QM$) formalism. A feature of the proposed approach consists in $N=4…
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its…
A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization.…
In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows to infer topological properties of the mechanical system, such as the occurrence of `floppy' boundary modes,…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the…
The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into…
Nonlinear (Polynomial, N-fold) SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is…
The association of the variational method with supersymmetric quantum mechanics through an ansatz for the superpotential is reviewed and the approximate energy spectra of non-exactly solvable potentials, such like the Hulthen, the Morse and…
The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As an example harmonic oscillator potential is…
Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the…