The Relativistic Linear Singular Oscillator
نویسندگان
چکیده
Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic limits. PACS numbers: 02.70.Bf, 03.65.Ca, 03.65.Pm Submitted to: J. Phys. A: Math. Gen.
منابع مشابه
Singular constrained linear systems
In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...
متن کاملHamilton-Jacobi Approach for Power-Law Potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, V (q) = αqn, where α and n are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of α, n and the total energy E. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometri...
متن کاملua nt - p h / 01 05 02 1 v 1 6 M ay 2 00 1 SPIN - ORBIT PENDULUM IN DIRAC OSCILLATOR ∗
The dynamics of wavepackets in a relativistic Dirac oscillator (DO) is considered. A comparison to nonrelativistic spin-orbit pendulum effect is discussed. Particular relativistic effects, like Zitterbewegung in spin motion, are found in Dirac representation. This trembling motion disappears in Foldy-Wouthuysen representation. A substantial difference between the dynamics of wavepackets corresp...
متن کاملThe variable-coefficient non-linear Schrödinger equation and the conformal properties of non-relativistic space-time
The cubic non-linear Schrödinger equation where the coefficient of the non-linear term can be a function F (t, x), is shown to pass the Painlevé test of Weiss, Tabor, and Carnevale only for F = (a+ bt)−1, where a and b are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to th...
متن کاملA Linear Approach to the Control of Vortex Induced Vibrations of Circular Cylinders with a 2-D Van der Pol Model for Structural Oscillator
In the present paper, a new 2-D Van der Polstructural oscillator model is introduced for the vortex induced vibrations of circular cylinders.The main purpose of this task is to control the recently introduced model by means of modern control definitions in state space. In order to control the system, the whole model is linearized about its equilibrium point by deriving state-space matrices. The...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003