The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As anâ€¦ (More)

A non-Hermitian complex symmetric 2 Ã— 2-matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of aâ€¦ (More)

The quantum mechanical brachistochrone system with a PT-symmetric Hamiltonian is Naimark-dilated and reinterpreted as a subsystem of a Hermitian system in a higher-dimensional Hilbert space. Thisâ€¦ (More)

New types of irreducible second order Darboux transformations for the one dimensional SchrÃ¶dinger equation are described. The main feature of such transformations is that the transformation functionsâ€¦ (More)

An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuousâ€¦ (More)

Concepts of supersymmetry and parasupersymmetry known for the one-dimensional stationary SchrÃ¶dinger equation are generalized to the time-dependent equation. Our approach is based on differentialâ€¦ (More)

Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantumâ€¦ (More)

The PT âˆ’symmetric (PTS) quantum brachistochrone problem is re-analyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting thisâ€¦ (More)

Recently (see quant-ph/0503040) an explicit example has been given of a PT -symmetric nondiagonalizable Hamiltonian. In this paper we show that such Hamiltonians appear as supersymmetric (SUSY)â€¦ (More)

The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated:â€¦ (More)