5,013 research outputs found
New Results and Matrix Representation for Daehee and Bernoulli Numbers and Polynomials
In this paper, we derive new matrix representation for Daehee numbers and
polynomials, the lambda-Daehee numbers and polynomials and the twisted Daehee
numbers and polynomials. This helps us to obtain simple and short proofs of
many previous results on Daehee numbers and polynomials. Moreover, we obtained
some new results for Daehee and Bernoulli numbers and polynomials
New Results on Higher-Order Daehee and Bernoulli Numbers and Polynomials
We derive new matrix representation for higher order Daehee numbers and
polynomials, the higher order lambda-Daehee numbers and polynomials and the
twisted lambda-Daehee numbers and polynomials of order k. This helps us to
obtain simple and short proofs of many previous results on higher order Daehee
numbers and polynomials. Moreover, we obtained recurrence relation, explicit
formulas and some new results for these numbers and polynomials. Furthermore,
we investigated the relation between these numbers and polynomials and Stirling
numbers, Norlund and Bernoulli numbers of higher order. The results of this
article gives a generalization of the results derived very recently by
El-Desouky and Mustafa [6]
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 -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 -weak-pseudo-Hermitian Hamiltonians. Using a
Liouvillean-type change of variables, the -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 -weak-pseudo-Hermitian reference-Hamiltonian
H(q)there is a set of exactly-solvable -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 -weak-pseudo-Hermitian isospectral
target-Hamiltonians are obtained.Comment: 11 pages, no figures
Position-dependent-mass; Cylindrical coordinates, separability, exact solvability, and PT-symmetry
The kinetic energy operator with position-dependent-mass in cylindrical
coordinates is obtained. The separability of the corresponding Schr\"odinger
equation is discussed within radial cylindrical mass settings. Azimuthal
symmetry is assumed and spectral signatures of various z-dependent interaction
potentials (Hermitian and non-Hermitian PT-symmetric) are reported.Comment: 16 page
Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential
The energy eigenvalues and the corresponding eigenfunctions of the
one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential
are analytically obtained within the position-dependent mass formalism. The
parametric generalization of the Nikiforov-Uvarov method is used in the
calculations by choosing a mass distribution.Comment: 10 page
Susceptibilities and speed of sound from PNJL model
We present the Taylor expansion coefficients of the pressure in quark number
chemical potential , for the strongly interacting
matter as described by the PNJL model for two light degenerate flavours of
quarks u and d. The expansion has been done upto eighth order in , and
the results are consistent with recent estimates from Lattice. We have further
obtained the specific heat , squared speed of sound and the
conformal measure \cC.Comment: 13 pages, 8 figures, References added, some discussions on Fig. 4
modified, one table added, results unchanged, version to appear in Phys. Rev.
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