Related papers: Spectral Design for Matrix Hamiltonians: Different…
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…
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant…
In this paper we continue studying of matrix $n\times n$ linear differential intertwining operators. The problems of minimization and of reducibility of matrix intertwining operators are considered and criterions of weak minimizability and…
A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target…
We generalize the standard first-order intertwining relationship of supersymmetric quantum mechanics in order to include simultaneous scaling transformations in both the original Hamiltonian and the intertwining operator. It is argued that…
We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\dagger]=0$ and $x^\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as…
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)…
The general solution of SUSY intertwining relations for three-dimensional Schr\"odinger operators is built using the class of second order supercharges with nondegenerate constant metric. This solution includes several models with arbitrary…
We present a novel approach for constructing quasi-isospectral higher-order Hamiltonians from time-independent Lax pairs by reversing the conventional interpretation of the Lax pair operators. Instead of treating the typically second-order…
The method of intertwining with n-dimensional (nD) linear intertwining operator L is used to construct nD isospectral, stationary potentials. It has been proven that differential part of L is a series in Euclidean algebra generators.…
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…
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of…
The Darboux transformation operator technique in differential and integral forms is applied to the generalized Schrodinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining…
The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger…
In exactly solvable quantum-mechanical systems, ladder and intertwining operators play a central role because, if they are found, the energy spectra can be obtained algebraically. In this paper, we propose the spectral intertwining relation…
General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in…
Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as…
In this paper we discuss a general strategy to construct vector coherent states of the Gazeau-Klauder type and we use them to built up examples of isospectral hamiltonians. For that we use a general strategy recently proposed by the author…
Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian $H_{-}=\omega(\xi^{\dag} \xi+\1/2)+\alpha \xi^{2}+\beta \xi^{\dag 2}$, where $\alpha \neq \beta$ and $\xi$ is a first order differential operator, to…
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…