Solutions of the Duffin–Kemmer–Petiau equation for a pseudoscalar potential step in (1 + 1) dimensions

We solve the Duffin–Kemmer–Petiau equation in the presence of a pseudoscalar potential step in (1 + 1) dimensions. We show that the paradox of Klein is not found for particles of spin-1, contrary to the case of the particles of spin-0 where it always persists. The absence of this paradox in the vector bosons is explained with the arguments based on effective mass.PACS Nos.: 03.65.Pm; 03.65.Ge

Application of the exact quantization rule for some noncentral separable potentials

The energy spectrum of some noncentral separable potentials are obtained using the exact quantization rule in r and θ dimensions. The results are consistent with those obtained by other methods. PACS Nos.: 03.65.Ca, 03.65.Ge

Semiclassical position and momentum information entropy for sech2 and a family of rational potentials

The classical and semiclassical position and momentum information entropies for the reflectionless sech2 potential and a family of rational potentials are obtained explicitly. The sum of these entropies is of interest for the entropic uncertainty principle that is stronger than the Heisenberg uncertainty relation. The analytic results relate the classical period of the motion, total energy, position and momentum entropy, and dependence upon the principal quantum number n. The logarithmic energy dependence of the entropies is presented. The potentials considered include as special cases the attractive delta function and square well. PACS Nos.: 03.67–a, 03.65.Sq, 03.65.Ge, 03.65.–w

Localized Excitations in a Dispersive Long Water-Wave System via an Extended Projective Approach

By means of an extended projective approach, a new type of variable separation excitation with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Based on the derived variable separation excitation, abundant localized coherent structures such as single-valued localized excitations, multiple-valued localized excitations and complex wave excitations are revealed by prescribing appropriate functions. - PACS numbers: 03.65.Ge, 05.45.Yv

Exact Green’S Function for 2D Dirac Oscillator in Constant Magnetic Field

The propagator of two-dimensional Dirac oscillator in the presence of a constant magnetic field is presented by means of path integrals, where the spin degree-of-freedom is described by odd Grassmannian variables and the gauge invariant part of the effective action has the form of the standard pseudoclassical action given by Berezin and Marinov. Then the path integration is carried out and the problem is solved exactly. The energy spectrum of the electron and the wave functions are extracted. - PACS numbers: 03.65.Ca, 03.65.Db, 03.65.Pm, 03.65.Ge.

The Fission, Fusion and Annihilation of Solitons of the (2+1)-Dimensional Broer-Kaup-Kupershmidt System

By means of an improved mapping approach, a series of excitations of the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific fission, fusion and annihilation phenomena of solitons are also obtained. - PACS numbers: 05.45.Yv, 03.65.Ge.

Energy-dependent point interaction: Self-adjointness

Recently, we constructed an energy-dependent point interaction (EDPI) in its most general form in one-dimensional quantum mechanics. In this paper, we show that stationary solutions of the Schrodinger equation with the EDPI form a complete set. Then any nonstationary solution of the time-dependent Schrodinger equation can be expressed as a linear combination of stationary solutions. This, however, does not necessarily mean that the EDPI is self-adjoint and the time-development of the nonstationary state is unitary. The EDPI is self-adjoint provided that the stationary solutions are all orthogonal to one another. We illustrate situations in which this orthogonality condition is not satisfied.PACS Nos.: 03.65.–w, 03.65.Nk, 03.65.Ge

Chaotic Solitons for the (2+1)-Dimensional Modified Dispersive Water-Wave System

With an improved mapping approach, a series of excitations of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave excitation, we obtain some special chaotic solitons. - PACS numbers: 05.45.Yv, 03.65.Ge

Exact Solutions and Solitons with Fission and Fusion Properties for the Generalized Broer-Kaup System

Starting from a Painlev´e-B¨acklund transformation and a linear variable separation approach, we obtain a quite general variable separation excitation to the generalized (2+1)-dimensional Broer-Kaup (GBK) system. Then based on the derived solution, we reveal soliton fission and fusion phenomena in the (2+1)-dimensional soliton system. - PACS numbers: 05.45.Yv, 03.65.Ge

Bell-Like and Peak-Like Loop Solitons in (2+1)-Dimensional Dispersive Long Water-Wave System

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Then based on the derived solution, we reveal some new types of loop solitons such as bell-like loop solitons and peak-like loop solitons in the (2+1)-dimensional DLW system. - PACS numbers: 05.45.Yv, 03.65.Ge