Coordinate asymptotics of the wave function for a system of four particles free in the initial state

1990 ◽  
Vol 82 (2) ◽  
pp. 157-169 ◽  
Author(s):  
S. L. Yakovlev
Keyword(s):  
Wave Function ◽  
Initial State ◽  
Coordinate Asymptotics

HIGH FREQUENCY LIMITS OF THE TWO-ELECTRON PHOTOIONIZATION CROSS SECTIONS

2002 ◽  
Vol 09 (02) ◽  
pp. 1161-1166 ◽  
Author(s):  
R. KRIVEC ◽  
M. YA. AMUSIA ◽  
V. B. MANDELZWEIG
Keyword(s):  
Wave Function ◽  
Excited States ◽  
Cross Sections ◽  
High Frequency ◽  
Nuclear Charge ◽  
Principal Quantum Number ◽  
Dipole Approximation ◽  
Wave Functions ◽  
Initial State ◽  
First Order

Several cross sections of two-electron processes at high but nonrelativistic photon energies ω are considered, which are expressed solely via the initial state wave function of the ionized two-electron object. The new high precision and locally correct nonvariational wave functions describing the ground and several lowest excited states of H -, He and helium-like ions are used in calculations of different cross sections in the pure dipole approximation and with account of first order corrections in ω/c2, and a number of the cross sections' ratios. The dependencies of all these quantities on the nuclear charge Z and the principal quantum number n (for 1 < n < 5) of the initial state excitation are studied.

scholarly journals Initial state and thermalization in the Color Glass Condensate framework

2015 ◽  
Vol 24 (10) ◽  
pp. 1530008 ◽  
Author(s):  
François Gelis
Keyword(s):  
Wave Function ◽  
Heavy Ion Collisions ◽  
Heavy Ion ◽  
High Energy ◽  
Color Glass ◽  
Color Glass Condensate ◽  
Nuclear Wave Function ◽  
Initial State ◽  
Early Stages ◽  
Ion Collisions

In this review, I present the description of the early stages of heavy ion collisions at high energy in the Color Glass Condensate framework, from the pre-collision high energy nuclear wave function to the point where hydrodynamics may start becoming applicable.

scholarly journals Boundary Bound Diffraction: A Combined Spectral and Bohmian Analysis

2018 ◽  
Author(s):  
Jalal Tounli ◽  
Aitor Alvarado ◽  
Ángel S. Sanz
Keyword(s):  
Wave Function ◽  
Optical Fibers ◽  
Spectral Decomposition ◽  
Matter Wave ◽  
Dynamical Analysis ◽  
Spinless Particle ◽  
Initial State ◽  
Relative Extension ◽  
Initial Wave Function ◽  
Localization Region

The diffraction-like process displayed by a spatially localized matter wave is here analyzed in a case where the free evolution is frustrated by the presence of hard-wall-type boundaries (beyond the initial localization region). The phenomenon is investigated in the context of a nonrelativistic, spinless particle with mass m confined in a one-dimensional box, combining the spectral decomposition of the initially localized wave function (treated as a coherent superposition of energy eigenfunctions) with a dynamical analysis based on the hydrodynamic or Bohmian formulation of quantum mechanics. Actually, such a decomposition has been used to devise a simple and efficient analytical algorithm that simplifies the computation of velocity fields (flows) and trajectories. As it is shown, the development of space-time patters inside the cavity depends on three key elements: the shape of the initial wave function, the mass of the particle considered, and the relative extension of the initial state with respect to the total length spanned by the cavity. From the spectral decomposition it is possible to identify how each one of these elements contribute to the localized matter wave and its evolution; the Bohmian analysis, on the other hand, reveals aspects connected to the diffraction dynamics and the subsequent appearance of interference traits, particularly recurrences and full revivals of the initial state, which constitute the source of the characteristic symmetries displayed by these patterns. It is also found that, because of the presence of confining boundaries, even in cases of increasingly large box lengths, no Fraunhofer-like diffraction features can be observed, as happens when the same wave evolves in free space. Although the analysis here is applied to matter waves, its methodology and conclusions are also applicable to confined modes of electromagnetic radiation (e.g., light propagating through optical fibers).

Coupled harmonic oscillators and their application in the dynamics of entanglement and the nonadiabatic Berry phases

2021 ◽  
Author(s):  
A. Abidi ◽  
A. Trabelsi ◽  
S. Krichene
Keyword(s):  
Wave Function ◽  
Coupling Parameter ◽  
Angular Frequency ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Logarithmic Scale ◽  
Initial State ◽  
Coupled Harmonic Oscillators ◽  
Berry Phases ◽  
Time Dependance

In the dynamic description of physical systems, the two coupled harmonic oscillators time-dependent mass, angular frequency and coupling parameter are recognized as a good working example. We present in this work an analytical treatment with a numerical evaluation of the entanglement and the nonadiabatic Berry phases in the vacuum state. On the basis of an exact resolution of the wave function solution of the time-dependent Schr¨odinger’s equation (T DSE) using the Heisenberg picture approach, we derive the wave function of the two coupled harmonic oscillators. At the logarithmic scale, we derive the entanglement entropies and the temperature. We discuss the existence of the cyclical initial state (CIS) based on an instant Hamiltonian and we obtain the corresponding nonadiabatic Berry phases through a period T. Moreover, we extend the result to case of N coupled harmonic oscillators. We use the numerical calculation to follow the dynamic evolution of the entanglement in comparison to the time dependance of the nonadiabatic Berry phases and the time dependance of the temperature. For two coupled harmonic oscillators with time-independent mass and angular frequency, the nonadiabatic Berry phases present a very slight oscillations with the equivalent period as the period of the entanglement. A second model is composed of two coupled harmonic oscillators with angular frequency which change initially as well as lately. Here in, the entanglement and the temperature exhibit the same oscillatory behavior with exponential increase in temperature.

RELATIVISTIC TREATMENT OF PHOTOEMISSION INCORPORATING THE SPATIALLY DEPENDENT PHOTON FIELD

1999 ◽  
Vol 06 (01) ◽  
pp. 145-149
Author(s):  
R. K. THAPA ◽  
SHIVRAJ GURUNG ◽  
ZAITHANZAUVA PACHUAU ◽  
D. T. KHATING
Keyword(s):  
Wave Function ◽  
Electronic States ◽  
Simple Theory ◽  
Initial State ◽  
Photon Field ◽  
State Wave ◽  
Relativistic Treatment

We discuss a simple theory of photoemission incorporating the relativistically defined initial state wave function for the electronic states. The photocurrent data are calculated in the case of tungsten and silicon.

A SCHEME FOR SPATIAL WAVE FUNCTION TELEPORTATION IN THREE DIMENSIONS

2006 ◽  
Vol 04 (05) ◽  
pp. 781-790
Author(s):  
O. AKHAVAN ◽  
A. T. REZAKHANI ◽  
M. GOLSHANI
Keyword(s):  
Wave Function ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Quantum Object ◽  
Initial State ◽  
N Level ◽  
Spatial Wave Function ◽  
Three Dimensional Space

We propose a theoretical scheme for teleportation of a general wave function of a quantum object. In principle, this protocol provides teleportation of discrete N-level spatial states of an object with various degrees of freedom, e.g. spin, in ordinary three-dimensional space. All necessary Bell states and their corresponding operators to measure and reconstruct the initial state are represented.

LIGHT QUARKONIA DECAYS IN THE CORRECTED 3P0 MODEL

2007 ◽  
Vol 16 (09) ◽  
pp. 2919-2922
Author(s):  
D. T. DA SILVA ◽  
J. N. QUADROS ◽  
M. L. L. DA SILVA ◽  
D. HADJIMICHEF
Keyword(s):  
Hilbert Space ◽  
Wave Function ◽  
Order Term ◽  
Pair Creation ◽  
Initial State ◽  
Relativistic Limit ◽  
New Model ◽  
Quantum Numbers ◽  
Decay Model ◽  
Space Formalism

The 3P0 model is a typical decay model which considers only OZI-allowed strong decays and considers a quark-antiquark pair creation in the presence of the initial state meson. The quark-antiquark pair is created with the vacuum quantum numbers. This model can also be obtained from the non-relativistic limit of the pair creation Hamiltonian. Applying the Reduced Hilbert Space formalism to the pair creation Hamiltonian will produce the characteristic expansion in powers of the wave function, where the 3P0 model is the lowest order term of this expansion. This new model will correct 3P0, which we call the Corrected 3P0 model or C 3P0 model. The model will be applied to the light quarkonia decay sector.

PHOTOFIELD EMISSION CALCULATIONS BY USING PROJECTION OPERATOR METHOD

2007 ◽  
Vol 21 (22) ◽  
pp. 1501-1507
Author(s):  
R. K. THAPA ◽  
GUNAKAR DAS ◽  
S. R. GURUNG ◽  
B. I. SHARMA ◽  
P. K. PATRA
Keyword(s):  
Wave Function ◽  
Group Theory ◽  
Matrix Element ◽  
Projection Operator ◽  
Operator Method ◽  
Emission Current Density ◽  
Initial State ◽  
Projection Operator Method ◽  
The Matrix ◽  
Dependent Vector

A model calculation of photofield emission is discussed in which initial state wave function has been deduced by using projection operator method of group theory. A spatial dependent vector potential is used to evaluate the matrix element for calculating the photofield emission current density.

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