35 research outputs found
First-order intertwining operators with position dependent mass and - weak-psuedo-Hermiticity generators
A Hermitian and an anti-Hermitian first-order intertwining operators are
introduced and a class of -weak-pseudo-Hermitian position-dependent mass
(PDM) Hamiltonians are constructed. A corresponding reference-target
-weak-pseudo-Hermitian PDM -- Hamiltonians' map is suggested. Some
-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models
are used as illustrative examples. Energy-levels crossing and flown-away states
phenomena are reported for the resulting Scarf II spectrum. Some of the
corresponding -weak-pseudo-Hermitian Scarf II- and
periodic-type-isospectral models (PT -symmetric and non-PT -symmetric) are
given as products of the reference-target map.Comment: 11 pages, no figures, Revised/Expanded, more references added. To
appear in the Int.J. Theor. Phy
(1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric
The effect of the built-in supersymmetric quantum mechanical language on the
spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and
complexified Lorentz scalar interactions, is re-emphasized. The signature of
the "quasi-parity" on the Dirac particles' spectra is also studied. A Dirac
particle with PDM and complexified scalar interactions of the form S(z)=S(x-ib)
(an inversely linear plus linear, leading to a PT-symmetric oscillator model),
and S(x)=S_{r}(x)+iS_{i}(x) (a PT-symmetric Scarf II model) are considered.
Moreover, a first-order intertwining differential operator and an
-weak-pseudo-Hermiticity generator are presented and a complexified
PT-symmetric periodic-type model is used as an illustrative example.Comment: 11 pages, no figures, revise
A new approach to the exact solutions of the effective mass Schrodinger equation
Effective mass Schrodinger equation is solved exactly for a given potential.
Nikiforov-Uvarov method is used to obtain energy eigenvalues and the
corresponding wave functions. A free parameter is used in the transformation of
the wave function. The effective mass Schrodinger equation is also solved for
the Morse potential transforming to the constant mass Schr\"{o}dinger equation
for a potential. One can also get solution of the effective mass Schrodinger
equation starting from the constant mass Schrodinger equation.Comment: 14 page
PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation
PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and
generalized harmonic oscillator potentials with the position-dependent mass. A
general point canonical transformation is applied by using a free parameter.
Three different forms of mass distributions are used. A set of the energy
eigenvalues of the bound states and corresponding wave functions for target
potentials are obtained as a function of the free parameter.Comment: 13 page
A Group-Theoretical Method for Natanzon Potentials in Position-Dependent Mass Background
A new manner for deriving the exact potentials is presented. By making use of
conformal mappings, the general expression of the effective potentials deduced
under su(1,1) algebra can be brought back to the general Natanzon
hypergeometric potentials
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
Exact solution of Effective mass Schrodinger Equation for the Hulthen potential
A general form of the effective mass Schrodinger equation is solved exactly
for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy
eigenvalues and the corresponding wave functions. A free parameter is used in
the transformation of the wave function.Comment: 9 page
An extended class of L2-series solutions of the wave equation
We lift the constraint of a diagonal representation of the Hamiltonian by
searching for square integrable bases that support an infinite tridiagonal
matrix representation of the wave operator. The class of solutions obtained as
such includes the discrete (for bound states) as well as the continuous (for
scattering states) spectrum of the Hamiltonian. The problem translates into
finding solutions of the resulting three-term recursion relation for the
expansion coefficients of the wavefunction. These are written in terms of
orthogonal polynomials, some of which are modified versions of known
polynomials. The examples given, which are not exhaustive, include problems in
one and three dimensions.Comment: 18 pages, 1 figur
Dilaton Dark Energy Model in f(R), f(T) and Horava-Lifshitz Gravities
In this work, we have considered dilaton dark energy model in Weyl-scaled
induced gravitational theory in presence of barotropic fluid. It is to be noted
that the dilaton field behaves as a quintessence. Here we have discussed the
role of dilaton dark energy in modified gravity theories namely, f(R); f(T) and
Horava-Lifshitz gravities and analyzed the behaviour of the dilaton field and
the corresponding potential in respect to these modified gravity theories
instead of Einstein's gravity. In f(R) and f(T) gravities, we have considered
some particular forms of f(R) and f(T) and we have shown that the potentials
always increase with the dilaton fields. But in Horava-Lifshitz gravity, it has
been seen that the potential always decreases as dilation field increases