Electron Escape from a Quantum Well

1996 ◽  
Vol 464 ◽  
Author(s):  
James P. Lavine ◽  
Harvey S. Picker
Keyword(s):  
Characteristic Time ◽  
Transition Probability ◽  
Bound State ◽  
Quantum Mechanical ◽  
Potential Well ◽  
Electron Systems ◽  
One Dimensional ◽  
First Order ◽  
Electron Escape ◽  
Free Transition

ABSTRACTThe quantum mechanical escape rate is calculated for an electron in a one-dimensional potential well. First-order time-dependent perturbation theory is used for the bound-to-bound and the bound-to-free transitions. The bound-to-free transition probability decays exponentially with bound energy. The fraction of one-electron systems in a bound state decays exponentially with time. The characteristic time constant grows exponentially with an increasein the depth of the potential well.

The Escape of Particles from a Quantum Well

1994 ◽  
Vol 366 ◽  
Author(s):  
James P. Lavine
Keyword(s):  
Characteristic Time ◽  
Bound State ◽  
Time Dependent ◽  
Rate Equations ◽  
Potential Well ◽  
Electron Systems ◽  
One Dimensional ◽  
First Order ◽  
Escape Problem ◽  
Well Depth

ABSTRACTThe escape rate is calculated for an electron in a one-dimensional potential well. First-order time-dependent perturbation theory is used with solutions of Schrödinger's equation and a set of coupled rate equations is numerically solved. The time evolution of an ensemble of one-electron systems is followed and the fraction of systems that remain in a bound state is found to decay exponentially as time passes. The characteristic time constant for the decay grows exponentially with an increase in the well depth. This is analogous to Kramers' result for the classical escape problem.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals Возбуждение и ионизация частицы в одномерной потенциальной яме нулевого радиуса предельно коротким световым импульсом

2022 ◽  
Vol 130 (3) ◽  
pp. 414
Author(s):  
Р.М. Архипов ◽  
М.В. Архипов ◽  
А.В. Пахомов ◽  
Н.Н. Розанов
Keyword(s):  
Wave Function ◽  
Energy Level ◽  
Short Pulse ◽  
Bound State ◽  
Characteristic Scale ◽  
Potential Well ◽  
One Dimensional ◽  
Characteristic Period ◽  
Zero Radius ◽  
Perturbation Approximation

The Migdal sudden perturbation approximation is used to solve the problem of excitation and ionization particles in a one-dimensional potential of zero radius with an extremely short pulse. There is has only one energy level in such a one-dimensional the delta-shaped potential well. It is shown that for pulse durations shorter than the characteristic period of oscillations of the wave function of the particle in the bound state, the population of the level (and the probability of ionization) is determined by the ratio of the electric the area of ​​the pulse to the characteristic “scale” of the area inversely proportional to the area of ​​localization of the particle in a bound state.

scholarly journals Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds

2020 ◽  
Vol 8 (1) ◽  
pp. 68-91
Author(s):  
Gianmarco Giovannardi
Keyword(s):  
Characteristic Direction ◽  
Fixed Degree ◽  
One Dimensional ◽  
First Order ◽  
Natural Choice ◽  
Higher Dimensional ◽  
Graded Manifold ◽  
The One ◽  
Graded Manifolds ◽  
Holonomy Map

AbstractThe deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

scholarly journals Perturbation Solution for One-Dimensional Flow to a Constant-Pressure Boundary in a Stress-Sensitive Reservoir

2021 ◽  
Author(s):  
Amarjot Singh Bhullar ◽  
Gospel Ezekiel Stewart ◽  
Robert W. Zimmerman
Keyword(s):  
Approximate Solution ◽  
Pore Pressure ◽  
Constant Pressure ◽  
Initial Permeability ◽  
Order Perturbation ◽  
Zeroth Order ◽  
One Dimensional ◽  
First Order ◽  
Outflow Boundary ◽  
Perturbation Solutions

Abstract Most analyses of fluid flow in porous media are conducted under the assumption that the permeability is constant. In some “stress-sensitive” rock formations, however, the variation of permeability with pore fluid pressure is sufficiently large that it needs to be accounted for in the analysis. Accounting for the variation of permeability with pore pressure renders the pressure diffusion equation nonlinear and not amenable to exact analytical solutions. In this paper, the regular perturbation approach is used to develop an approximate solution to the problem of flow to a linear constant-pressure boundary, in a formation whose permeability varies exponentially with pore pressure. The perturbation parameter αD is defined to be the natural logarithm of the ratio of the initial permeability to the permeability at the outflow boundary. The zeroth-order and first-order perturbation solutions are computed, from which the flux at the outflow boundary is found. An effective permeability is then determined such that, when inserted into the analytical solution for the mathematically linear problem, it yields a flux that is exact to at least first order in αD. When compared to numerical solutions of the problem, the result has 5% accuracy out to values of αD of about 2—a much larger range of accuracy than is usually achieved in similar problems. Finally, an explanation is given of why the change of variables proposed by Kikani and Pedrosa, which leads to highly accurate zeroth-order perturbation solutions in radial flow problems, does not yield an accurate result for one-dimensional flow. Article Highlights Approximate solution for flow to a constant-pressure boundary in a porous medium whose permeability varies exponentially with pressure. The predicted flowrate is accurate to within 5% for a wide range of permeability variations. If permeability at boundary is 30% less than initial permeability, flowrate will be 10% less than predicted by constant-permeability model.

Approximate approaches to the one-dimensional finite potential well

2011 ◽  
Vol 32 (6) ◽  
pp. 1701-1710 ◽  
Author(s):  
Shilpi Singh ◽  
Praveen Pathak ◽  
Vijay A Singh
Keyword(s):  
Potential Well ◽  
One Dimensional ◽  
The One

Bound State of Electrons in a One-Dimensional Chain

1994 ◽  
Vol 182 (1) ◽  
pp. 89-96 ◽  
Author(s):  
L. S. Brizhik ◽  
A. A. Eremko
Keyword(s):  
Bound State ◽  
Dimensional Chain ◽  
One Dimensional

scholarly journals NEW L1-GRADIENT TYPE ESTIMATES OF SOLUTIONS TO ONE-DIMENSIONAL QUASILINEAR PARABOLIC SYSTEMS

2010 ◽  
Vol 12 (01) ◽  
pp. 85-106 ◽  
Author(s):  
S. N. ANTONTSEV ◽  
J. I. DÍAZ
Keyword(s):  
Type Equation ◽  
Parabolic Type ◽  
Parabolic Systems ◽  
Diffusion Term ◽  
One Dimensional ◽  
First Order ◽  
Estimates Of Solutions ◽  
Gradient Type ◽  
Degenerate Type ◽  
Parabolic Type Equation

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L1-gradient type estimates for its solutions which are uniform in the sense that they do not depend on the coefficients nor on the size of the spatial domain. We also give some applications of such estimates to gas dynamics, filtration problems, a p-Laplacian parabolic type equation and some first order systems of Hamilton–Jacobi or conservation laws type.

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