Related papers: The Harmonic Oscillator in the Framework of Scale …
A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…
Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a…
We study the generalized harmonic oscillator which has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for…
We study a harmonic molecule confined to a one--dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare…
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle…
We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the…
The nonlinear, cubic Schrodinger (NLS) equation has numerous physical applications, but in general is very difficult to solve. Nonetheless, under certain circumstances parameters quantifying the width, momentum and energy of the…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of…
An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like…
We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schr\"odinger picture. Generally in the most papers of the literature, the inverted harmonic oscillator is formally obtained from the harmonic…
The one-particle three-dimensional Dirac equation with spherical symmetry is solved for the Hulthen potential. The s-wave relativistic energy spectrum and two-component spinor wavefunctions are obtained analytically. Conforming to the…
High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schr\"{o}dinger equation is cast into nonlinear Riccati equation, which is solved analytically in first…
The frequency of a classical periodic system can be obtained using action variables without solving the dynamical equations. We demonstrate the construction of two equivalent forms of the action variable for a one dimensional relativistic…
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…
Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in…