共查询到20条相似文献,搜索用时 31 毫秒
1.
An approximation method, namely, the Extended Wronskian
Determinant Approach, is suggested to study the one-dimensional
Dirac equation. An integral equation, which can be solved by
iterative procedure to find the wave functions, is established. We
employ this approach to study the one-dimensional Dirac equation
with one-well potential, and give the energy levels and wave
functions up to the first order iterative approximation. For
double-well potential, the energy levels up to the first order
approximation are given. 相似文献
2.
In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show
how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave
equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We find Lie and Noether point symmetries of the corresponding
wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy,
linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations
on a flat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonflat manifolds. 相似文献
3.
Guy Richard Kol 《Optical and Quantum Electronics》2017,49(11):385
We predict the emergence of rogue wave solutions in one-dimensional exciton–polariton condensates under homogeneous pumping. We model the condensate dynamics in a microwire using the dissipative Gross–Pitaevskii equation for the polariton field, with considers attractive nonlinearity, coupled to the rate equation of the excitonic reservoir density. With the help of the direct ansatz method and similarity transformation, deformed first order rogue wave solutions are constructed and its dynamics analyzed. We show that the deformed rogue wave has a curved background controlled by the pump power and the strength of the nonlinear interaction of polaritons. Moreover, the maximal population of the polaritons appears where high energy of rogue wave is concentrated. 相似文献
4.
H. H. Azizbekyan A. M. Manukyan V. M. Mekhitarian A. M. Ishkhanyan 《Journal of Contemporary Physics (Armenian Academy of Sciences)》2018,53(4):279-285
The variety of bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle is presented. The physical potentials and energy spectrum of this wave equation are related to those for a corresponding Schrödinger equation in the sense that all the potentials derived for the latter equation are also applicable for the wave equation under consideration. We show that in contrast to the Schrödinger equation the characteristic spatial length of the potential imposes a restriction on the energy spectrum that directly reflects the uncertainty principle. Studying the inversesquare- root bi-confluent Heun potential, it is shown that the uncertainty principle limits, from below, the principal quantum number for the bound states, i.e., physically feasible states have an infimum cut so that the ground state adopts a higher quantum number as compared to the Schrödinger case. 相似文献
5.
Ashfaque H. Bokhari A. H. Kara M. Karim F. D. Zaman 《International Journal of Theoretical Physics》2009,48(7):1919-1928
In this paper we discuss symmetries of a nonlinear wave equation that arises as a consequence of some Riemannian metrics of
signature −2. The objective of this study is to show how geometry can be responsible in giving rise to a nonlinear inhomogeneous
wave equation rather than assuming nonlinearities in the wave equation from physical considerations. We find Lie point symmetries
of the corresponding wave equations and give their solutions in two cases. Some interesting physical conclusions relating
to conservation laws such as energy, linear and angular momenta are also determined. 相似文献
6.
陈子栋 《原子与分子物理学报》2005,22(3):483-487
本文求解了在球坐标下Hartmann势的Schrdinger方程,得到了能量方程和归一化的波函数.用Laplace变换使径向的二阶微分方程退化为一阶微分方程,直接积分后用级数展开,应用Laplace逆变换得出本征函数.讨论了径向本征函数的像函数的递推关系,从而得出径向波函数的递推关系. 相似文献
7.
In this Letter, we investigate the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution. 相似文献
8.
Davood Momeni 《Physics letters. A》2019,383(14):1543-1548
We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge. 相似文献
9.
We considered the propagation of laser monochromatic radiation in a superlattice that contains regions with an elevated concentration
of carriers. The model of the energy spectrum of electrons is chosen in the strong coupling approximation. The electromagnetic
field is described quasiclassically with Maxwell equations, which, as applied to the problem under study, are reduced to a
non-one-dimensional sine-Gordon wave equation for the vector-potential. We analyzed the wave equation in the approximation
of slowly varying amplitudes and phases and obtained and numerically solved an effective equation that describes the electromagnetic
field in the superlattice. We studied different regimes of propagation of laser radiation, analyzed diffraction by regions
with an elevated electron concentration. 相似文献
10.
E. Tobisch 《Journal of Experimental and Theoretical Physics》2014,119(2):359-365
We consider nonlinear gravity-capillary waves with the nonlinearity parameter ? ~ 0.1–0.25. For this nonlinearity, time scale separation does not occur and the kinetic wave equation does not hold. An energy cascade in this case is built at the dynamic time scale (D-cascade) and is computed by the increment chain equation method first introduced in [15]. We for the first time compute an analytic expression for the energy spectrum of nonlinear gravity-capillary waves as an explicit function of the ratio of surface tension to the gravity acceleration. We show that its two limits—pure capillary and pure gravity waves on a fluid surface—coincide with the previously obtained results. We also discuss relations of the D-cascade model with a few known models used in the theory of nonlinear waves such as Zakharov’s equation, resonance of modes with nonlinear Stokes-corrected frequencies, and the Benjamin-Feir index. These connections are crucial in understanding and forecasting specifics of the energy transport in a variety of multicomponent wave dynamics, from oceanography to optics, from plasma physics to acoustics. 相似文献
11.
Summary The formation of envelope solitons is discussed in a relativistic plasma under the influence of a fluctuating electric field.
We use the kinetic-theory approach for our analysis. Due to the larger inertia, only the electrons are considered to be relativistic
and the ions to be nonrelativistic. A NLS equation is derived describing the motion of the solitary wave. This NLS equation
actually comes from an approximation of a pair of equations which can be considered to be a relativistic generalisation of
the Zakharov equation. We next discuss the exact form of the envelope solitary-wave solution of the NLS equation and the modulation
stability of such a wave. When the density, momentum and energy of such wave packets are fixeda priori, conditions are derived for the parameters of the problem from such stability consideration. 相似文献
12.
13.
李介平 《原子与分子物理学报》2002,19(1):15-18
光场下类氢原子的Schrdinger方程可用缀饰势方法求解.波动方程展开为Floquet分波后,可以得到弱光场或强光场下近似的径向波函数和复的电离本征值,然后计算了共振能量和半宽度. 相似文献
14.
A. V. Tsvetkova 《Russian Journal of Mathematical Physics》2016,23(4):536-550
In the paper, the Cauchy problem for the wave equation on singular spaces of constant curvature and on an infinite homogeneous tree is studied. Two singular spaces are considered: the first one consists of a three-dimensional Euclidean space to which a ray is glued, and the other is formed by two three-dimensional Euclidean spaces joined by a segment. The solution of the Cauchy problem for the wave equation on these objects is described and the behavior of the energy of a wave as time tends to infinity is studied.The Cauchy problem for the wave equation on an infinite homogeneous tree is also considered, where the matching conditions for the Laplace operator at the vertices are chosen in the form generalizing the Kirchhoff conditions. The spectrum of such an operator is found, and the solution of the Cauchy problem for the wave equation is described. The behavior of wave energy as time tends to infinity is also studied. 相似文献
15.
Exact solutions of the Klein—Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform
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Sami Ortakaya 《中国物理 B》2012,21(7):70303-070303
We present exact solutions for the Klein-Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation. 相似文献
16.
E. A. Kopylova 《Russian Journal of Mathematical Physics》2010,17(2):226-239
We obtain a dispersive long-time decay with respect to weighted energy norms for solutions of the 2D wave equation with generic potential. The decay extends results obtained by Murata for the 2D Schrödinger equation. 相似文献
17.
We consider the propagation of super-Gaussian monochromatic laser beams in a three-dimensional array of quantum dots coupled
by the tunneling effect along one axis. The electron energy spectrum of the system corresponds to the Hubbard model, where
the Coulomb interaction of electrons in quantum dots is taken into account. The field of the laser beam is described by the
Maxwell equations, from which a nonhomogeneous wave equation for the vector potential is obtained. In the approximation of
slowly varying amplitudes and phases, the wave equation is reduced to a phenomenological equation describing the electromagnetic
field in an array of chains of quantum dots. We study the influence of the system parameters and the frequency of the laser-beam
field on the propagation in the medium by solving numerically the phenomenological equation. We obtain the dependence of the
factor characterizing the diffraction blooming of the beam in an array of chains of quantum dots on the parameters of the
system’s electron energy spectrum. 相似文献
18.
《Physics letters. [Part B]》2006,641(5):357-361
We consider a Brans–Dicke cosmology in five-dimensional space–time. Neglecting the quadratic and the mixed Brans–Dicke terms in the Einstein equation, we derive a modified wave equation of the Brans–Dicke field. We show that, at high energy limit, the 3-brane Brans–Dicke cosmology could be described as the standard one by changing the equation of state. Finally as an illustration of the purpose, we show that the dark energy component of the universe agrees with the observations data. 相似文献
19.
20.
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale. 相似文献