3,916 research outputs found
Supersymmetric approach to exactly solvable systems with position-dependent effective masses
We discuss the relationship between exact solvability of the Schr\"{o}dinger
equation with a position-dependent mass and the ordering ambiguity in the
Hamiltonian operator within the frame of supersymmetric quantum mechanics. The
one-dimensional Schr\"{o}dinger equation, derived from the general form of the
effective mass Hamiltonian, is solved exactly for a system with exponentially
changing mass in the presence of a potential with similar behaviour, and the
corresponding supersymmetric partner Hamiltonians are related to the
effective-mass Hamiltonians proposed in the literature.Comment: 12 pages article in LaTEX (uses standard article.sty). Please check
http://www1.gantep.edu.tr/~ozer for other studies of Nuclear Physics Group at
University of Gaziantep. [arXiv admin note: excessive overlap with
quant-ph/0306065 and "Supersymmetric approach to quantum systems with
position-dependent effective mass" by A. R. Plastino, A. Rigo, M. Casas, F.
Garcias, and A. Plastino - Phys. Rev. A 60, 4318 - 4325 (1999)
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
Knee complaints vary with age and gender in the adult population. Population-based reference data for the Knee injury and Osteoarthritis Outcome Score (KOOS)
BACKGROUND: Self-reported knee complaints may vary with age and gender. Reference data from the adult population would help to better interpret the outcome of interventions due to knee complaints. The objectives of the present study were to describe the variation of self-reported knee pain, function and quality of life with age and gender in the adult population and to establish population-based reference data for the Knee injury and Osteoarthritis Outcome Score (KOOS). METHODS: Population-based cohort retrieved from the national population register. The knee-specific Knee injury and Osteoarthritis Outcome Score (KOOS) was mailed to 840 subjects aged 18â84 yrs. RESULTS: 68% response rate. Women in the age group 55â74 reported more knee-related complaints in all the KOOS subscales than age-matched men. The differences were significant for the subscales Pain (p = 0.027), Symptoms (p = 0.003) and ADL function (p = 0.046). In men, worse ADL and Sport and Recreation function was seen in the oldest age group 75â84 years compared to the younger age groups (p < 0.030). In women, worse Pain (p < 0.007), ADL (p < 0.030), Sport and Recreation (p < 0.001) and QOL (p < 0.002) were seen already in the age group 55â74 compared to the younger age groups. CONCLUSION: We found pain and other symptoms, physical function, and knee-related quality of life to vary with age and gender implying the use of age- and gender matched reference values for improved understanding of the outcome after interventions due to knee injury and knee OA
(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
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
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
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
On two superintegrable nonlinear oscillators in N dimensions
We consider the classical superintegrable Hamiltonian system given by
, where U
is known to be the "intrinsic" oscillator potential on the Darboux spaces of
nonconstant curvature determined by the kinetic energy term T and parametrized
by {\lambda}. We show that H is Stackel equivalent to the free Euclidean
motion, a fact that directly provides a curved Fradkin tensor of constants of
motion for H. Furthermore, we analyze in terms of {\lambda} the three different
underlying manifolds whose geodesic motion is provided by T. As a consequence,
we find that H comprises three different nonlinear physical models that, by
constructing their radial effective potentials, are shown to be two different
nonlinear oscillators and an infinite barrier potential. The quantization of
these two oscillators and its connection with spherical confinement models is
briefly discussed.Comment: 11 pages; based on the contribution to the Manolo Gadella Fest-60
years-in-pucelandia, "Recent advances in time-asymmetric quantum mechanics,
quantization and related topics" hold in Valladolid (Spain), 14-16th july
201
Approximate Solution of the effective mass Klein-Gordon Equation for the Hulthen Potential with any Angular Momentum
The radial part of the effective mass Klein-Gordon equation for the Hulthen
potential is solved by making an approximation to the centrifugal potential.
The Nikiforov-Uvarov method is used in the calculations. Energy spectra and the
corresponding eigenfunctions are computed. Results are also given for the case
of constant mass.Comment: 12 page
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