Pseudo-Hermiticity as a generalization of usual Hermiticity is a rather common feature of (differential) operators emerging in various physical setups. Examples are Hamiltonians of PTand CPT-symmetric quantum mechanical systems [1] as well as the operator of the spherically symmetric α-dynamo [2] in magnetohydrodynamics (MHD). In order to solve the inverse spectral problem for these operators, ...

The approach of multi-dimensional SUSY Quantum Mechanics is used in an explicit construction of exactly solvable 3-body ( and quasi-exactly-solvable N -body ) matrix problems on a line. From intertwining relations with time-dependent operators, we build exactly solvable non-stationary scalar and 2 × 2 matrix 3-body models which are time-dependent extensions of the Calogero model. Finally, we in...

In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral self-adjoint operators living in different Hilbert spaces. Many examples are discussed in details. Many of them arise from the theory of frames in Hilbert spaces, other...

In this work, we have extended the factorization method of scalar shape-invariant Schrödinger Hamiltonians to a class Dirac-like matrix Hamiltonians. The intertwining operators equations been implemented in shape invariant equations. We considered also another kind anti-intertwining changing sign energy. can be obtained from reduction higher dimensional spin systems. Two examples worked out, on...