Related papers: Solution of Second Order Supersymmetrical Intertwi…
We propose a new kind of supersymmetric (SUSY) transformation in the case of the two-channel scattering problem with equal thresholds, for partial waves of the same parity. This two-fold transformation is based on two imaginary…
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…
The Coulomb branch of $N=2$ supersymmetric gauge theories in four dimensions is described in general by an integrable Hamiltonian system in the holomorphic sense. A natural construction of such systems comes from two-dimensional gauge…
Supersymmetry offers one of the deepest insights in the concept of solvability in quantum mechanics. This insight is, paradoxically, restricted by one of the most serious formal drawbacks of the standard Witten's formulation of…
Recently (see quant-ph/0503040) an explicit example has been given of a PT-symmetric non-diagonalizable Hamiltonian. In this paper we show that such Hamiltonians appear as supersymmetric (SUSY) partners of Hermitian (hence diagonalizable)…
We construct supersymmetric (SUSY) generalized MIC-Kepler system and show that the systems with half integral Dirac quantization condition \mu= \pm{1/2}, \pm{3/2}, \pm{5/2},..... belong to a SUSY family (hierarchy of Hamiltonian) with same…
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSY--QM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of…
Supersymmetric (SUSY) transformation operators corresponding to complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. Obtained results are applied to…
The application of N=2 supersymmetric quantum mechanics for the quantization of homogeneous systems coupled with gravity is discussed. Starting with the superfield formulation of an N=2 SUSY sigma model, Hermitian self-adjoint expressions…
We study complex potentials and related non-diagonalizable Hamiltonians with special emphasis on formal definitions of associated functions and Jordan cells. The nonlinear SUSY for complex potentials is considered and the theorems…
We investigate for the N = 2 supersymmetry (SUSY) a relation between a vector supermultiplet of the linear SUSY and the Volkov-Akulov model of the nonlinear SUSY. We express component fields of the vector supermultiplet in terms of…
A simple way to find solutions of the Painlev\'e IV equation is by identifying Hamiltonian systems with third-order differential ladder operators. Some of these systems can be obtained by applying supersymmetric quantum mechanics (SUSY QM)…
We show explicitly in D = 2 that N = 2 nonlinear supersymmetric (SUSY) Volkov-Akulov model is equivalent to a spontaneously broken N = 2 linear SUSY interacting theory containing the ordinary Yukawa interactions and mass terms, which is…
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…
Abundant second-order maximally conformally superintegrable Hamiltonian systems are re-examined, revealing their underlying natural Weyl structure and offering a clearer geometric context for the study of St\"ackel transformations (also…
It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…
The aim of this letter is to compute the evolution of some expected values, such as the field operators $a^\pm$, quadratures and atomic inversion, under supersymmetric (SUSY) partner Hamiltonians associated to the Jaynes-Cummings…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
A novel algebraic topology approach to supersymmetry (SUSY) and symmetry breaking in quantum field and quantum gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear…
The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite…