Classical and quantum quasi-free position dependent mass; P\"oschl-Teller and ordering-ambiguity

We argue that the classical and quantum mechanical correspondence may play a basic role in the fixation of the ordering-ambiguity parameters. We use quasi-free position-dependent masses in the classical and quantum frameworks. The effective P\"oschl-Teller model is used as a manifested reference potential to elaborate on the reliability of the ordering-ambiguity parameters available in the literature.Comment: 10 page

Non-Hermitian von Roos Hamiltonian's η\eta-weak-pseudo-Hermiticity, isospectrality and exact solvability

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type change of variables, the $\eta$-weak-pseudo-Hermitian von Roos Hamiltonians H(x) are mapped into the traditional Schrodinger Hamiltonian form H(q), where exact isospectral correspondence between H(x) and H(q) is obtained. Under a user-friendly position dependent mass settings, it is observed that for each exactly-solvable $\eta$-weak-pseudo-Hermitian reference-Hamiltonian H(q)there is a set of exactly-solvable $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians H(x). A non-Hermitian PT-symmetric Scarf II and a non-Hermitian periodic-type PT-symmetric Samsonov-Roy potentials are used as reference models and the corresponding $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians are obtained.Comment: 11 pages, no figures

d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.Comment: 14 pages, no figures, to appear in J. Phys. A: Math. Ge

Non-Hermitian Hamiltonian versus E=0 localized states

We analyze the zero energy solutions, of a two dimensional system which undergoes a non-radial symmetric, complex potential V(r,$\phi$). By virtue of the coherent states concept, the localized states are constructed, and the consequences of the imaginary part of the potential are found both analytically and schematically.Comment: 12 pages, 10 figure

Ordering ambiguity revisited via position dependent mass pseudo-momentum operators

Ordering ambiguity associated with the von Roos position dependent mass (PDM) Hamiltonian is considered. An affine locally scaled first order differential introduced, in Eq.(9), as a PDM-pseudo-momentum operator. Upon intertwining our Hamiltonian, which is the sum of the square of this operator and the potential function, with the von Roos d-dimensional PDM-Hamiltonian, we observed that the so-called von Roos ambiguity parameters are strictly determined, but not necessarily unique. Our new ambiguity parameters' setting is subjected to Dutra's and Almeida's [11] reliability test and classified as good ordering.Comment: 10 pages, no figures, revised/expanded, mathematical presentations in section 2 (Especially, the typological Errors in Eqs.(9)-(12))are now corrected. To appear in the Int. J. Theor. Phy