JMP: Quantum Mechanics (General and Nonrelativistic)

Delay time in quaternionic quantum mechanics

Stefano De Leo and Gisele Ducati
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. Our study shows the energy region which amplifies the difference between quaternionic and complex quantum mechanics. ... [J. Math. Phys. 53, 022102 (2012)] published Mon Feb 13, 2012.

Convergence of expansions in Schrodinger and Dirac eigenfunctions, with an application to the R-matrix theory

Julia Stasinska
Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schrodinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the pre ... [J. Math. Phys. 53, 022101 (2012)] published Thu Feb 2, 2012.

[script PT] symmetric, Hermitian and [script P]-self-adjoint operators related to potentials in [script PT] quantum mechanics

Tomas Ya. Azizov and Carsten Trunk
In the recent years, a generalization H = p + x(ix) of the harmonic oscillator using a complex deformation was investigated, where epsilon is a real parameter. Here, we will consider the most simple case: epsilon even and x real. We will give a complete characterization of three different classes of ... [J. Math. Phys. 53, 012109 (2012)] published Tue Jan 31, 2012.

The trace formula for a point scatterer on a compact hyperbolic surface

Henrik Ueberschar
An exact trace formula for the perturbation of the Laplacian by a Dirac delta potential on a compact hyperbolic Riemann surface is derived. The formula can be considered an analogue of the Selberg trace formula. The difference of perturbed and unperturbed trace is expressed as an identity term plus ... [J. Math. Phys. 53, 012108 (2012)] published Mon Jan 30, 2012.

Coherences of accelerated detectors and the local character of the Unruh effect

Charis Anastopoulos and Ntina Savvidou
We study the locality of the acceleration temperature in the Unruh effect. To this end, we develop a new formalism for the modeling of macroscopic irreversible detectors. In particular, the formalism allows for the derivation of the higher-order coherence functions, analogous to the ones employed in ... [J. Math. Phys. 53, 012107 (2012)] published Mon Jan 30, 2012.

Generalization of H-pseudoalgebraic structures

Qinxiu Sun
The goal of this paper is to study Hom-H-pseudoalgebraic structures generalizing H-pseudoalgebras of associative and Lie type. We provide examples of the new structures and present some properties and construction theorems. Similar to the case of H-pseudoalgebras, the annihilator algebras are also d ... [J. Math. Phys. 53, 012105 (2012)] published Wed Jan 18, 2012.

Notes on the Riccati operator equation in open quantum systems

Bartlomiej Gardas and Zbigniew Puchala
A recent problem [B. Gardas, J. Math. Phys. 52, 042104 (2011)] concerning an antilinear solution of the Riccati equation is solved. We also exemplify that a simplification of the Riccati equation, even under reasonable assumptions, can lead to a not equivalent equation. ... [J. Math. Phys. 53, 012106 (2012)] published Wed Jan 18, 2012.

Compound transfer matrices: Constructive and destructive interference

Petarpa Boonserm and Matt Visser
Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the particle can be ignored, the transmission probability of the co ... [J. Math. Phys. 53, 012104 (2012)] published Tue Jan 17, 2012.

Phase coherent states with circular Jacobi polynomials for the pseudoharmonic oscillator

Zouhair Mouayn
We construct a class of generalized phase coherent states |e; gamma, alpha, [eh] >, indexed by points e of the unit circle and depending on three positive parameters gamma, alpha, and [eh], by replacing the labeling coefficient z/sqrt(n!) of the canonical coherent states by circular Jacobi polynomia ... [J. Math. Phys. 53, 012103 (2012)] published Tue Jan 10, 2012.

Quasi-coherent states for harmonic oscillator with time-dependent parameters

Nuri Unal
In this study, we discuss the harmonic oscillator with the time-dependent frequency, omega(t), and the mass, M(t), by generalizing the holomorphic coordinates for the harmonic oscillator. In general cases, we solve the Schrodinger equation by reducing it into the Riccati equation and discuss the unc ... [J. Math. Phys. 53, 012102 (2012)] published Fri Jan 6, 2012.

The gap equation for spin-polarized fermions

Abraham Freiji, Christian Hainzl, and Robert Seiringer
We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (delta/T) <= 2, with T the temperature and delta the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear ope ... [J. Math. Phys. 53, 012101 (2012)] published Wed Jan 4, 2012.

Prepotential approach to solvable rational extensions of Harmonic Oscillator and Morse potentials

C.-L. Ho
We show how the recently discovered solvable rational extensions of Harmonic Oscillator and Morse potentials can be constructed in a direct and systematic way, without the need of supersymmetry, shape invariance, Darboux-Crum, and Darboux-Backlund transformations. ... [J. Math. Phys. 52, 122107 (2011)] published Fri Dec 30, 2011.

The propagator of the attractive delta-Bose gas in one dimension

Sylvain Prolhac and Herbert Spohn
We consider the quantum delta-Bose gas on the infinite line. For repulsive interactions, Tracy and Widom have obtained an exact formula for the quantum propagator. In our contribution we explicitly perform its analytic continuation to attractive interactions. We also study the connection to the expa ... [J. Math. Phys. 52, 122106 (2011)] published Fri Dec 30, 2011.

Relativistic and nonrelativistic bound states of the isotonic oscillator by Nikiforov-Uvarov method

Sameer M. Ikhdair and Ramazan Sever
A nonpolynomial one-dimensional quantum potential in the form of an isotonic oscillator (harmonic oscillator with a centripetal barrier) is studied. We provide the nonrelativistic bound state energy spectrum E and the wave functions psi(x) in terms of the associated Laguerre polynomials in the frame ... [J. Math. Phys. 52, 122108 (2011)] published Fri Dec 30, 2011.

Exact results for finite quantum Hall systems of electrons at filling factor one: Disk geometry

Orion Ciftja
We obtain exact analytical expressions for the total energy per particle and related quantities corresponding to a finite quantum Hall system of electrons in a disk geometry when filling factor of the Landau level is one. Such exact results apply to finite systems of electrons with an arbitrary numb ... [J. Math. Phys. 52, 122105 (2011)] published Thu Dec 29, 2011.

Spectral problems for the Weyl-ordered form of operators ((1/p-hat))q-hat

M. Gianfreda and G. Landolfi
In this paper, we consider quantization of powers of the ratio between the Hamiltonian coordinates for position and momentum in one-dimensional systems. The domain of the operators consists of square integrable functions over a finite real interval to ensure boundedness and self-adjointness. The spe ... [J. Math. Phys. 52, 122104 (2011)] published Wed Dec 28, 2011.

An alternative approach to Schrodinger equations with a spatially varying mass

M. Capak and B. Gonul
Extending the point canonical transformation approach in a manner distinct from the previous ones, we propose a unified approach of generating potentials of all classes having non-constant masses. ... [J. Math. Phys. 52, 122103 (2011)] published Fri Dec 23, 2011.

Extreme covariant quantum observables in the case of an Abelian symmetry group and a transitive value space

Erkka Theodor Haapasalo and Juha-Pekka Pellonpaa
We represent quantum observables as normalized positive operator valued measures and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group G. The value space of such observables is a transitive G-space. We charact ... [J. Math. Phys. 52, 122102 (2011)] published Wed Dec 21, 2011.

On the supremum and infimum of bounded quantum observables

Long Long and Shifang Zhang
Let S([script H]) be the set of all bounded self-adjoint linear operators on a complex Hilbert space [script H]. In 2006, Gudder [Math. Slovaca 56, 573 (2006)] introduced a new order [curly precedes, eq] on S([script H]). Since then, the existence conditions and representations of the supremum and i ... [J. Math. Phys. 52, 122101 (2011)] published Tue Dec 20, 2011.

New approximate method to solve the Schrodinger equation with a Woods-Saxon-like potential

Guozhong Wang, Hui Li, Yifeng Shen, and Biqin Dong
We presented a new method to solve Schrodinger equations especially for two special kinds of potentials, which are named the first and second kind of Woods-Saxon-like potentials in this paper. The Woods-Saxon-like potential characterized by a rapid increase occurred at the system's boundary varies s ... [J. Math. Phys. 52, 112105 (2011)] published Tue Nov 29, 2011.

Euclidean Jordan algebras, hidden actions, and J-Kepler problems

Guowu Meng
For a simple euclidean Jordan algebra, let [fraktur co] be its conformal algebra, [script P] be the manifold consisting of its semi-positive rank-one elements, C([script P]) be the space of complex-valued smooth functions on [script P]. An explicit action of [fraktur co] on C([script P]), referred t ... [J. Math. Phys. 52, 112104 (2011)] published Wed Nov 16, 2011.