1,110 research outputs found
How to prepare quantum states that follow classical paths
We present an alternative quantization procedure for the one-dimensional
non-relativistic quantum mechanics. We show that, for the case of a free
particle and a particle in a box, the complete classical and quantum
correspondence can be obtained using this formulation. The resulting wave
packets do not disperse and strongly peak on the classical paths. Moreover, for
the case of the free particle, they satisfy minimum uncertainty relation.Comment: 10 pages, 3 figures, to appear in Europhysics Letter
Optimized basis expansion as an extremely accurate technique for solving time-independent Schr\"odinger equation
We use the optimized trigonometric finite basis method to find energy
eigenvalues and eigenfunctions of the time-independent Schrodinger equation
with high accuracy. We apply this method to the quartic anharmonic oscillator
and the harmonic oscillator perturbed by a trigonometric anharmonic term as not
exactly solvable cases and obtain the nearly exact solutions.Comment: 11 pages, 4 figure
Generalized Uncertainty Principle and the Ramsauer-Townsend Effect
The scattering cross section of electrons in noble gas atoms exhibits a
minimum value at electron energies of approximately 1eV. This is the
Ramsauer-Townsend effect. In this letter, we study the Ramsauer-Townsend effect
in the framework of the Generalized Uncertainty Principle.Comment: 11 pages, 3 figure
Minimal Length and the Quantum Bouncer: A Nonperturbative Study
We present the energy eigenvalues of a quantum bouncer in the framework of
the Generalized (Gravitational) Uncertainty Principle (GUP) via quantum
mechanical and semiclassical schemes. In this paper, we use two equivalent
nonperturbative representations of a deformed commutation relation in the form
[X,P]=i\hbar(1+\beta P^2) where \beta is the GUP parameter. The new
representation is formally self-adjoint and preserves the ordinary nature of
the position operator. We show that both representations result in the same
modified semiclassical energy spectrum and agrees well with the quantum
mechanical description.Comment: 14 pages, 2 figures, to appear in Int. J. Theor. Phy
Modification of Coulomb's law in closed spaces
We obtain a modified version of Coulomb's law in two- and three-dimensional
closed spaces. We demonstrate that in a closed space the total electric charge
must be zero. We also discuss the relation between total charge neutrality of a
isotropic and homogenous universe to whether or not its spatial sector is
closed.Comment: 11 pages, 3 figure
Quantum Stephani exact cosmological solutions and the selection of time variable
We study perfect fluid Stephani quantum cosmological model. In the present
work the Schutz's variational formalism which recovers the notion of time is
applied. This gives rise to Wheeler-DeWitt equation for the scale factor. We
use the eigenfunctions in order to construct wave packets for each case. We
study the time-dependent behavior of the expectation value of the scale factor,
using many-worlds and deBroglie-Bohm interpretations of quantum mechanics.Comment: 19 pages, 7 figure
- …