Related papers: Extended SUSY quantum mechanics, intertwining oper…
Motivated by the duality of normalizable states and the presence of the quasi-parity quantum number q=+/-1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied.…
We build the coherent states for a family of solvable singular Schr\"odinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their…
This is a series of 5 lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory…
We construct the family of spin chain Hamiltonians, which have affine quantum group symmetry. Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to affine…
In this study, we investigate the stationary states of the Glauber-Fock oscillator waveguide array. We begin by transforming the associated Hamiltonian into the form of a quantum harmonic oscillator Hamiltonian, allowing the implementation…
Nonlinear SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. Possible multidimensional extensions of Nonlinear SUSY are described. The full classification of ladder-reducible and irreducible…
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…
We review some basic elements on k-fermions, which are objects interpolating between bosons and fermions. In particular, we define k-fermionic coherent states and study some of their properties. The decomposition of a Q-uon into a boson and…
We show that for the strictly isospectral Hamiltonians, the corresponding coherent states are related by a unitary transformation. As an illustration, we discuss, the example of strictly isospectral one-dimensional harmonic oscillator…
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…
This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some…
Quantum Mechanics SUper-SYmmetry (QM-SUSY) provides a general framework for studies using phenomenological potentials for nucleons (or clusters) interacting with a core. The SUSY potentials result from the transformation of the mean field…
The general solution of SUSY intertwining relations of first order for two-dimensional Schr\"odinger operators with position-dependent (effective) mass is built in terms of four arbitrary functions. The procedure of separation of variables…
For a symmetric pair $(G,H)$ of reductive groups we extend to a large class of generalized principal series representations our previous construction of meromorphic families of symmetry breaking operators. These operators intertwine between…
We discuss two distinct aspects in supersymmetric quantum mechanics. First, we introduce a new class of operators A and $\bar{A}$ in terms of anticommutators between the momentum operator and N+1 arbitrary superpotentials. We show that…
We introduce a new technique for dealing with the matrix elements of the Hamiltonian operator in loop quantum gravity, based on the use of intertwiners projected on coherent states of angular momentum. We give explicit expressions for the…
The connection between the strictly isospectral construction in supersymmetric quantum mechanics and the general zero mode solutions of the Schroedinger equation is explained by introducing slightly generalized first-order intertwining…
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…
In this paper, a geometric process to compare solutions of symmetric hyperbolic systems on (possibly different) globally hyperbolic manifolds is realized via a family of intertwining operators. By fixing a suitable parameter, it is shown…
Generalizing a recent proposal leading to one-parameter families of Hamiltonians and to new sets of squeezed states, we construct larger classes of physically admissible Hamiltonians permitting new developments in squeezing. Coherence is…