We study the D-dimensional Schr6dinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov （NU） method, we calculate ...We study the D-dimensional Schr6dinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov （NU） method, we calculate the corresponding eigenfunctions and eigenvalues.展开更多
We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general fe...We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.展开更多
In order to study the effect of large scale cosmological expansion on small systems, we assume a Friedmann- Robertson-Walker type coordinate system in presence of a nonzero cosmological constant and derive a non-stati...In order to study the effect of large scale cosmological expansion on small systems, we assume a Friedmann- Robertson-Walker type coordinate system in presence of a nonzero cosmological constant and derive a non-static Reissner-Nrdstr6m metric. It is an analytic function of r for all values except at r = O, which is singular. By determining the equation of motion in this metric we can estimate how expansion of the universe may affect Pioneer＇s motion. Because the metric does not have any event horizon and so high potential regions are accessible, this may help us in better understanding AGN phenomenon.展开更多
In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V ...In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V with all non-zero components and the static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor det R ≠0. It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. It also covers our previous results as a spacial case. Some new metrics admitting proper Ricci collineations are also investigated.展开更多
We study space-time transformations of the time-dependent Schrodingerequation (TDSE) with time- and position-dependent (effective) mass. We obtain the most generalspace-time transformation that maps such a TDSE onto a...We study space-time transformations of the time-dependent Schrodingerequation (TDSE) with time- and position-dependent (effective) mass. We obtain the most generalspace-time transformation that maps such a TDSE onto another one of its kind. The transformedpotential is given in explicit form.展开更多
Specific modifications of the usual canonical commutation relations between position and momentumoperators have been proposed in the literature in order to implement the idea of the existence of a minimal observablele...Specific modifications of the usual canonical commutation relations between position and momentumoperators have been proposed in the literature in order to implement the idea of the existence of a minimal observablelength. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentumspace representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and thecorresponding momentum space wave function are obtained. Following Chang et al. (Phys. Rev. D 65 (2002) 125027),we discuss constraint that can be placed on the minimal length by measuring the energy levels of an electron in a penningtrap.展开更多
We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein–Gordon and Dirac equations with equal vector and scalar potentials, and try to fi...We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein–Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.展开更多
In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by re...In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by reciprocal transformations.Based on the Lax-pair of the Calogero–Bogoyavlenskii–Schiff equation,a non-isospectral Lax-pair of the(2+1)-dimensional Hunter–Saxton equation is derived.In addition,exact singular solutions with a finite number of corners are obtained.Furthermore,the(2+1)-dimensional μ-Hunter–Saxton equation is presented,and its exact peaked traveling wave solutions are derived.展开更多
文摘We study the D-dimensional Schr6dinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov （NU） method, we calculate the corresponding eigenfunctions and eigenvalues.
文摘We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.
基金0ur thanks go to the Isfahan University of Technology for the financial support.
文摘In order to study the effect of large scale cosmological expansion on small systems, we assume a Friedmann- Robertson-Walker type coordinate system in presence of a nonzero cosmological constant and derive a non-static Reissner-Nrdstr6m metric. It is an analytic function of r for all values except at r = O, which is singular. By determining the equation of motion in this metric we can estimate how expansion of the universe may affect Pioneer＇s motion. Because the metric does not have any event horizon and so high potential regions are accessible, this may help us in better understanding AGN phenomenon.
文摘In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V with all non-zero components and the static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor det R ≠0. It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. It also covers our previous results as a spacial case. Some new metrics admitting proper Ricci collineations are also investigated.
文摘We study space-time transformations of the time-dependent Schrodingerequation (TDSE) with time- and position-dependent (effective) mass. We obtain the most generalspace-time transformation that maps such a TDSE onto another one of its kind. The transformedpotential is given in explicit form.
文摘Specific modifications of the usual canonical commutation relations between position and momentumoperators have been proposed in the literature in order to implement the idea of the existence of a minimal observablelength. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentumspace representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and thecorresponding momentum space wave function are obtained. Following Chang et al. (Phys. Rev. D 65 (2002) 125027),we discuss constraint that can be placed on the minimal length by measuring the energy levels of an electron in a penningtrap.
基金Supported in part by National Natural Science Foundation of China under Grant Nos.11247274 and 11075115supported by Fundamental Research Funds for the Central Universities under Grant No.3122013k003
文摘We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein–Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.
基金Supported by National Natural Science Foundation of China under Grant No.11471174NSF of Ningbo under Grant No.2014A610018
文摘In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by reciprocal transformations.Based on the Lax-pair of the Calogero–Bogoyavlenskii–Schiff equation,a non-isospectral Lax-pair of the(2+1)-dimensional Hunter–Saxton equation is derived.In addition,exact singular solutions with a finite number of corners are obtained.Furthermore,the(2+1)-dimensional μ-Hunter–Saxton equation is presented,and its exact peaked traveling wave solutions are derived.
