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

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.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x20501407 ◽

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.

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Electron Escape from a Quantum Well

MRS Proceedings ◽

10.1557/proc-464-275 ◽

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.

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Relativistic Energy Analysis of Five-Dimensionalq-Deformed Radial Rosen-Morse Potential Combined withq-Deformed Trigonometric Scarf Noncentral Potential Using Asymptotic Iteration Method

Advances in High Energy Physics ◽

10.1155/2016/7910341 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 8

Author(s):

Subur Pramono ◽

A. Suparmi ◽

Cari Cari

Keyword(s):

Wave Function ◽

Energy Level ◽

Quantum Number ◽

Iteration Method ◽

Morse Potential ◽

Bound State ◽

Asymptotic Iteration Method ◽

Relativistic Energy ◽

Radial Wave ◽

Orbital Quantum Number

We study the exact solution of Dirac equation in the hyperspherical coordinate under influence of separableq-deformed quantum potentials. Theq-deformed hyperbolic Rosen-Morse potential is perturbed byq-deformed noncentral trigonometric Scarf potentials, where all of them can be solved by using Asymptotic Iteration Method (AIM). This work is limited to spin symmetry case. The relativistic energy equation and orbital quantum number equationlD-1have been obtained using Asymptotic Iteration Method. The upper radial wave function equations and angular wave function equations are also obtained by using this method. The relativistic energy levels are numerically calculated using Matlab, and the increase of radial quantum numberncauses the increase of bound state relativistic energy level in both dimensionsD=5andD=3. The bound state relativistic energy level decreases with increasing of both deformation parameterqand orbital quantum numbernl.

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The Escape of Particles from a Quantum Well

MRS Proceedings ◽

10.1557/proc-366-353 ◽

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.

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Quantum Boxes, Stringed Instruments

10.1093/oso/9780198808275.003.0008 ◽

2017 ◽

Author(s):

Frank S. Levin

Keyword(s):

Energy Level ◽

Schrödinger Equation ◽

Quantum System ◽

Schrodinger Equation ◽

Probability Distributions ◽

Wave Functions ◽

Energy Level Diagram ◽

One Dimensional ◽

Stringed Instruments ◽

Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

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