Related papers: Time-Dependent Gaussian Solution for the Kostin Eq…
We consider time-dependent Gaussian wave packet solutions of the Schrodinger equation (with arbitrary initial central position, x_0, and momentum, p_0, for an otherwise free-particle, but with an infinite wall at x=0, so-called bouncing…
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
The work considers the damped Pinney equation, defined as the model arising when a linear in velocity damping term is included in the Pinney equation. In the general case the resulting equation does not admit Lie point symmetries or is…
Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
We reexamine the general solution of a Schr\"{o}dinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
Homogeneous time-dependent solutions of massive gravity generalise the plane wave solutions of the linearised Fierz-Pauli equations for a massive spin-two particle, as well as the Kasner solutions of General Relativity. We show that they…
Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative system. Here, as an application of this formalism, we consider a dissipative system of charged…
The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes by directly solving the time-dependent Schrodinger equation as a differential equation. In this work, we provide an alternative way…
We discuss the time development of Gaussian wave packet solutions of the quantum bouncer' (a quantum mechanical particle subject to a uniform downward force, above an impermeable flat surface). We focus on the evaluation and visualization…
In the present paper we consider the semiclassical magnetic Schr\"odinger equation, which describes the dynamics of charged particles under the influence of a electro-magnetic field. The solution of the time-dependent Schr\"odinger equation…
We derive an exact analytical solution to the time-dependent Schr\"odinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet…
The time-evolution of the maximum and the width of exact analytic wave packet (WP) solutions of the time-dependent Schr\"odinger equation (SE) represents the particle and wave aspects, respectively, of the quantum system. The dynamics of…
In this paper we discuss some aspects of the theory of wave packets. We consider a popular non-covariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic…
Exact solutions of several nonstationary problems of quantum mechanics are obtained. It is shown that if the initial conditions of the problem correspond to the localized-in-space particle, then it moves exactly along the classical…
In this paper we study a general nonlinear Schr\"odinger equation with a time dependent harmonic potential. Despite the lack of traslational invariance we find a symmetry trasformation which, up from any solution, produces infinitely many…