scholarly journals Inconstant Planck’s constant

2015 ◽  
Vol 30 (34) ◽  
pp. 1550209 ◽  
Author(s):  
Gianpiero Mangano ◽  
Fedele Lizzi ◽  
Alberto Porzio
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Electromagnetic Fields ◽  
Free Particle ◽  
Mean Value ◽  
Fundamental Constants ◽  
Quantum Structure ◽  
Planck Constant ◽  
One Dimensional ◽  
Variance Formula

Motivated by the Dirac idea that fundamental constants are dynamical variables and by conjectures on quantum structure of space–time at small distances, we consider the possibility that Planck constant [Formula: see text] is a time depending quantity, undergoing random Gaussian fluctuations around its measured constant mean value, with variance [Formula: see text] and a typical correlation timescale [Formula: see text]. We consider the case of propagation of a free particle and a one-dimensional harmonic oscillator coherent state, and show that the time evolution in both cases is different from the standard behavior. Finally, we discuss how interferometric experiments or exploiting coherent electromagnetic fields in a cavity may put effective bounds on the value of [Formula: see text].

scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

scholarly journals Classical path from quantum motion for a particle in a transparent box

2014 ◽  
Vol 36 (2) ◽  
Author(s):  
Salvatore De Vincenzo
Keyword(s):  
Undergraduate Students ◽  
Free Particle ◽  
Mean Value ◽  
Position Operator ◽  
One Dimensional ◽  
Quantum Numbers ◽  
Classical Path ◽  
The Mean ◽  
Basic Ideas ◽  
Quantum Motion

We consider the problem of a free particle inside a one-dimensional box with transparent walls (or equivalently, along a circle with a constant speed) and discuss the classical and quantum descriptions of the problem. After calculating the mean value of the position operator in a time-dependent normalized complex general state and the Fourier series of the function position, we explicitly prove that these two quantities are in accordance by (essentially) imposing the approximation of high principal quantum numbers on the mean value. The presentation is accessible to advanced undergraduate students with a knowledge of the basic ideas of quantum mechanics.

scholarly journals A geodesical approach for the harmonic oscillator

2020 ◽  
Vol 17 (1 Jan-Jun) ◽  
pp. 6
Author(s):  
Rodrigo Sánchez-Martínez ◽  
Alvaro Lorenzo Salas-Brito ◽  
Hilda Noemí Núñez-Yépez
Keyword(s):  
Harmonic Oscillator ◽  
Kepler Problem ◽  
Spherical Surface ◽  
Free Particle ◽  
Theoretical Physics ◽  
Canonical Transformations ◽  
Canonical Coordinates ◽  
One Dimensional ◽  
Particle Form ◽  
The One

The harmonic oscillator (HO) is present in all contemporary physics, from elementary classical mechanicsto quantum field theory. It is useful in general to exemplify techniques in theoretical physics. In this work,we use a method for solving classical mechanic problems by first transforming them to a free particle formand using the new canonical coordinates to reparametrize its phase space. This technique has been used tosolve the one-dimensional hydrogen atom and also to solve for the motion of a particle in a dipolar potential.Using canonical transformations we convert the HO Hamiltonian to a free particle form which becomestrivial to solve. Our approach may be helpful to exemplify how canonical transformations may be used inmechanics. Besides, we expect it will help students to grasp what they mean when it is said that a problemhas been transformed into another completely different one. As, for example, when the Kepler problem istransformed into free (geodesic) motion on a spherical surface.

PERELOMOV AND BARUT–GIRARDELLO SU(1, 1) COHERENT STATES FOR HARMONIC OSCILLATOR IN ONE-DIMENSIONAL HALF SPACE

2006 ◽  
Vol 21 (12) ◽  
pp. 2635-2644 ◽  
Author(s):  
Q. H. LIU ◽  
H. ZHUO
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Half Space ◽  
Ground State ◽  
Classical Limit ◽  
Coherent States ◽  
Mean Values ◽  
One Dimensional ◽  
The Mean

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

scholarly journals Chaotic dynamics of a free particle interacting linearly with a harmonic oscillator

2005 ◽  
Vol 208 (1-2) ◽  
pp. 96-114 ◽  
Author(s):  
Stephan De Bièvre ◽  
Paul E. Parris ◽  
Alex Silvius
Keyword(s):  
Harmonic Oscillator ◽  
Chaotic Dynamics ◽  
Free Particle

One-dimensional coherent-state representation on a circle in phase space

1994 ◽  
Vol 50 (5) ◽  
pp. 4293-4297 ◽  
Author(s):  
P. Domokos ◽  
P. Adam ◽  
J. Janszky
Keyword(s):  
Phase Space ◽  
Coherent State ◽  
State Representation ◽  
One Dimensional

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

scholarly journals Quantum gravity: Physics from supergeometries

2014 ◽  
Vol 11 (08) ◽  
pp. 1450067 ◽  
Author(s):  
Diego Julio Cirilo-Lombardo ◽  
Thiago Prudêncio
Keyword(s):  
Black Hole ◽  
Coherent State ◽  
Line Element ◽  
Black Hole Entropy ◽  
Quantum Structure ◽  
Geometrical Object ◽  
Large N ◽  
General Basis ◽  
The Relationship ◽  
Classical Radiation

We show that the metric (line element) is the first geometrical object to be associated to a discrete (quantum) structure of the spacetime without necessity of black hole-entropy-area arguments, in sharp contrast with other attempts in the literature. To this end, an emergent metric solution obtained previously in [ Phys. Lett. B661 (2008) 186–191] from a particular non-degenerate Riemannian superspace is introduced. This emergent metric is described by a physical coherent state belonging to the metaplectic group Mp (n) with a Poissonian distribution at lower n (number basis) restoring the classical thermal continuum behavior at large n(n → ∞), or leading to non-classical radiation states, as is conjectured in a quite general basis by means of the Bekenstein–Mukhanov effect. Group-dependent conditions that control the behavior of the macroscopic regime spectrum (thermal or not), as the relationship with the problem of area/entropy of the black hole are presented and discussed.

scholarly journals Parameter Estimation of a Class One-Dimensional Discrete Chaotic System

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Lidong Liu ◽  
Jinfeng Hu ◽  
Huiyong Li ◽  
Jun Li ◽  
Zishu He ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Chaotic System ◽  
Chaos Control ◽  
Mean Value ◽  
Unknown Parameters ◽  
Tent Map ◽  
One Dimensional ◽  
Chebyshev Map ◽  
Mean Value Method ◽  
Control And Synchronization

It is of vital importance to exactly estimate the unknown parameters of chaotic systems in chaos control and synchronization. In this paper, we present a method for estimating one-dimensional discrete chaotic system based on mean value method (MVM). It is proposed by exploiting the ergodic and synchronization features of chaos. It can effectively estimate the parameter value, and it is more exact than MVM. Finally, numerical simulations on Chebyshev map and Tent map show that the proposed method has better performance of parameter estimation than MVM.

Theory of pseudogaps in charge density waves in application to photo electron spectroscopy

2002 ◽  
Vol 12 (9) ◽  
pp. 73-73
Author(s):  
S. I. Matveenko ◽  
S. Brazovskii
Keyword(s):  
Charge Density ◽  
Adiabatic Approximation ◽  
Free Particle ◽  
Charge Density Waves ◽  
Photon Absorption ◽  
Electronic Excitations ◽  
Dimensional Electron ◽  
Density Waves ◽  
One Dimensional ◽  
Exponential Decrease

For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron - phonon interactions these processes are described by ronlinear configurations of an instanton type. We calculate the subgap absorption as it can be observed by means of photo electron or tunneling spectroscopies. In details we consider systems with gapless modes: 1D semiconductors with acoustic phonons and incommensurate charge density waves. We found that below the free particle edge the pseudogap starts with the exponential decrease of transition rates changing to a power law deeply within the pseudogap, near the absolute edge.

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