We show that and how the centrifugal-singularity paradox [first formulated by Jevicki and Rodriguez in Phys. Lett. B 146 (1984) 55, partially resolved by Das and Pernice in Nucl. Phys. B 561 (1999) 357 and covering, as its l = 0 special case, also the half-oscillator problem discussed, recently, by Gangopadhyaya and Mallow (arXiv: hep-th/0206133) and by Das and Pernice in their subsequent comme...

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the F th power of a conserved charge: H = Q with F = 2, 3, ... . This construction, called fractional supersymmetric quantum mechanics, was realized in terms of a paragrassmann variable θ of order F , which satisfies θ = 0. Here, we present an alternative realization of such an algebra in which the int...

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT -symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermit...

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel’fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed. SUSY (supersymmetry) is a concept which connects between bo...

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT -symmetric non-Hermitian Hamiltonians studied in the literature are pseudo-Hermitian and argue that the structure responsible for the reality of the spectrum of these Hamiltonian is their pseudo-Hermiticity not PT -symmetry. We explore the basic pr...

We review recent results on how to extend the supersymmetry SUSY formalism in Quantum Mechanics to linear generalizations of the time-dependent Schrödinger equation in (1+1) dimensions. The class of equations we consider contains many known cases, such as the Schrödinger equation for position-dependent mass. By evaluating intertwining relations, we obtain explicit formulas for the interrelation...

We propose an extension of supersymmetric quantum mechanics which produces a family of isospectral hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given. Further, we show how to build up vector coherent states of the Gazeau-Klauder type associated to our hamiltonians.

Dong Ruan∗ Department of Physics, Tsinghua University, Beijing 100084, P. R. China, Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou, 730000, P. R. China The Key Laboratory of Quantum Information and Measurements of Ministry of Education, Tsinghua University, Beijing 100084, P. R. China, and Weicheng Huang Institute of Applied Chemistry, Xingjiang Uni...

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 operators. We also present a multiple-parameter generalization of the strictly isospectral construction in the same perspective. PACS 03.65-Quantum mechanics.