680 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
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
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
Quantum cosmology with varying speed of light: canonical approach
We investigate --dimensional cosmology with varying speed of light.
After solving corresponding Wheeler-DeWitt equation, we obtain exact solutions
in both classical and quantum levels for (--)--dominated Universe.
We then construct the ``canonical'' wave packets which exhibit a good classical
and quantum correspondence. We show that arbitrary but appropriate initial
conditions lead to the same classical description. We also study the situation
from de-Broglie Bohm interpretation of quantum mechanics and show that the
corresponding Bohmian trajectories are in good agreement with the classical
counterparts.Comment: 14 pages, 7 figures, to appear in Physics Letters
Detrended Fluctuation analysis of Bach's Inventions and Sinfonias pitches
Detrended Fluctuation Analysis (DFA), suitable for the analysis of
nonstationary time series, is used to investigate power law in some of the
Bach's pitches series. Using DFA method, which also is a well-established
method for the detection of long-range correlations, frequency series of Bach's
pitches have been analyzed. In this view we find same Hurts exponents in the
range (0.7-0.8) in his Inventions and sinfonia.Comment: 5 pages, 4 figure
On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
Different candidates of Quantum Gravity such as String Theory, Doubly Special
Relativity, Loop Quantum Gravity and black hole physics all predict the
existence of a minimum observable length or a maximum observable momentum which
modifies the Heisenberg uncertainty principle. This modified version is usually
called the Generalized (Gravitational) Uncertainty Principle (GUP) and changes
all Hamiltonians in quantum mechanics. In this Letter, we use a recently
proposed GUP which is consistent with String Theory, Doubly Special Relativity
and black hole physics and predicts both a minimum measurable length and a
maximum measurable momentum. This form of GUP results in two additional terms
in any quantum mechanical Hamiltonian, proportional to and
, respectively, where is the GUP
parameter. By considering both terms as perturbations, we study two quantum
mechanical systems in the framework of the proposed GUP: a particle in a box
and a simple harmonic oscillator. We demonstrate that, for the general
polynomial potentials, the corrections to the highly excited eigenenergies are
proportional to their square values. We show that this result is exact for the
case of a particle in a box.Comment: 11 pages, to appear in Europhysics Letter
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