Related papers: Solution of Second Order Supersymmetrical Intertwi…
Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two…
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…
The problem of d-dimensional Schrodinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H, H_1) of intertwined Hamiltonians one can associate another pair of…
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlev\'e IV and Painlev\'e V equations…
Supersymmetry (SUSY) in non-relativistic quantum mechanics (QM) is applied to a 2-dimensional physical system: a neutron in an external magnetic field. The superpotential and the two-component wave functions of the ground state are found…
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the…
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first…
The problem of intertwined Hamiltonians in two dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane,Minkowski plane, Poincar{\' e} half plane ($AdS_2$), de Sitter Plane ($dS_2$), sphere, and torus. It…
Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term…
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…
Among the list of one dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen--Morse II potential. The first objective is to analyze the scattering matrix corresponding to this potential. We show that it includes a series…
We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV…
The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are…
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…
We study intertwining relations for matrix one-dimensional, in general, non-Hermitian Hamiltonians by matrix differential operators of arbitrary order. It is established that for any matrix intertwining operator Q_N^- of minimal order N…
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
We continue our investigation of the nonlinear SUSY for complex potentials started in the Part I (math-ph/0610024) and prove the theorems characterizing its structure in the case of non-diagonalizable Hamiltonians. This part provides the…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…