Polynomial supersymmetry for matrix Hamiltonians

The Wkb Approximation for General Matrix Hamiltonians

We present a method of obtaining WKB type solutions for generalized .~ Schroedinger equations for which the Hamiltonian is an arbitrary matrix function of any.number of pairs of canonical operators. Our solution reduces the problem to that of finding the matrix which diagonalizes the classical Hamiltonian and determining the scalar WKB wave functions for the diagonalized Hamiltonian's entries (...

Differential Polynomial Rings of Triangular Matrix Rings

Hurwitz Matrix for Polynomial Matrices

If a system is given by its transfer function then the stability of the system is determined hy the denominator polynomial and its corresponding Hurwitz matrix 7-{. Also the critical stability conditions are determined by its determinant det 7-{. The aim of this paper is to get a generalized Hurwitz matrix for polynomial matrices. In order to achieve that, we first obtain a relation between the...

Horizons of stability in matrix Hamiltonians

Non-Hermitian Hamiltonians H 6= H possess the real (i.e., observable) spectra inside certain specific, “physical” domains of parameters D = D(H). In general, the determination of their “observability-horizon” boundaries ∂D is difficult. We list the pseudo-Hermitian real N by N matrix Hamiltonians for which the “prototype” horizons ∂D are defined by closed analytic formulae.

Polynomial Heisenberg algebras and higher order supersymmetry

It is shown that the higher order supersymmetric partners of the harmonic oscillator Hamiltonian provide the simplest non-trivial realizations of the polynomial Heisenberg algebras. A linearized version of the corresponding annihilation and creation operator leads to a Fock representation which is the same as for the harmonic oscillator Hamiltonian. 1. Introduction. The non-linear algebras have...