Modified Gaussian Wave Packet Method for Calculating Initial State Wave Functions in Photodissociation

2018 ◽  
Vol 14 (11) ◽  
pp. 5527-5534 ◽  
Author(s):  
Shanyu Han ◽  
Daiqian Xie ◽  
Hua Guo
Keyword(s):  
Wave Packet ◽  
Wave Functions ◽  
Gaussian Wave Packet ◽  
Initial State ◽  
State Wave

Gaussian wave packet states of a generalized inverted harmonic oscillator with time-dependent mass and frequency

2015 ◽  
Vol 93 (8) ◽  
pp. 841-845 ◽  
Author(s):  
I.A. Pedrosa ◽  
Alberes Lopes de Lima ◽  
Alexandre M. de M. Carvalho
Keyword(s):  
Wave Packet ◽  
Harmonic Oscillator ◽  
Uncertainty Relation ◽  
Quantum Correlations ◽  
Wave Functions ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Order Ordinary Differential Equation ◽  
Quantum Invariant ◽  
Dependent Mass

We derive quantum solutions of a generalized inverted or repulsive harmonic oscillator with arbitrary time-dependent mass and frequency using the quantum invariant method and linear invariants, and write its wave functions in terms of solutions of a second-order ordinary differential equation that describes the amplitude of the damped classical inverted oscillator. Afterwards, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum, the associated uncertainty relation, and the quantum correlations between coordinate and momentum. As a particular case, we apply our general development to the generalized inverted Caldirola–Kanai oscillator.

Electron Correlations Observed Through Intensity Interferometry: Study of Model Initial State Wave Functions

2001 ◽  
Vol T92 (1) ◽  
pp. 447 ◽  
Author(s):  
B. Feuerstein ◽  
M. Schulz ◽  
R. Moshammer ◽  
J. Ullrich
Keyword(s):  
Wave Functions ◽  
Electron Correlations ◽  
Initial State ◽  
Intensity Interferometry ◽  
State Wave

scholarly journals Survival probability in Generalized Rosenzweig-Porter random matrix ensemble

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Giuseppe De Tomasi ◽  
Mohsen Amini ◽  
Soumya Bera ◽  
Ivan Khaymovich ◽  
Vladimir Kravtsov
Keyword(s):  
Wave Packet ◽  
Thermodynamic Limit ◽  
Survival Probability ◽  
Wave Functions ◽  
Initial State ◽  
Extended Phase ◽  
Periodic Oscillations ◽  
Power Law Decay ◽  
Matrix Ensemble ◽  
Random Matrix Ensemble

We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability \bm{R(t)}𝐑(𝐭), the probability of finding the initial state after time \bm{t}𝐭. In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that \bm{R(t)}𝐑(𝐭) can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of \bm{R(t)}𝐑(𝐭) with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of \bm{R(t\to\infty)=k}𝐑(𝐭→∞)=𝐤, finite in the thermodynamic limit \bm{N\rightarrow\infty}𝐍→∞, which approaches \bm{k=R(t\to 0)}𝐤=𝐑(𝐭→0) in this limit.

Self-consistent calculation of excited3P state wave functions of atoms

1971 ◽  
Vol 5 (6) ◽  
pp. 647-655 ◽  
Author(s):  
P. K. Mukherjee ◽  
A. K. Bhattacharya ◽  
A. Mukherji
Keyword(s):  
Wave Functions ◽  
Consistent Calculation ◽  
State Wave ◽  
Self Consistent

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

scholarly journals Exponential decay of bound state wave functions

1973 ◽  
Vol 32 (4) ◽  
pp. 319-340 ◽  
Author(s):  
A. J. O'Connor
Keyword(s):  
Exponential Decay ◽  
Bound State ◽  
Wave Functions ◽  
State Wave

GEOMETRIC PHASES, SQUEEZED QUANTUM STATES AND GAUSSIAN WAVE PACKET STATES OF RELIC GRAVITONS

2012 ◽  
Vol 18 ◽  
pp. 13-17
Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO
Keyword(s):  
Wave Packet ◽  
Linear Time ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Geometric Phases ◽  
Uncertainty Product ◽  
Quantized Field ◽  
Generalized Time

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

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