Comments on “Agreement between Classical and Quantum Mechanical Solutions for a Linear Potential inside a One-Dimensional Infinite Potential Well”

1969 ◽  
Vol 37 (12) ◽  
pp. 1287-1288 ◽  
Author(s):  
Noble M. Johnson ◽  
John N. Churchill
Keyword(s):  
Quantum Mechanical ◽  
Linear Potential ◽  
Potential Well ◽  
One Dimensional ◽  
Infinite Potential Well

Quantum complexity associated with tunneling

2019 ◽  
Vol 19 (3&4) ◽  
pp. 222-236
Author(s):  
Ofir Flom ◽  
Asher Yahalom ◽  
Haggai Zilberberg ◽  
L.P. Horwitz ◽  
Jacob Levitan
Keyword(s):  
Quantum Effect ◽  
Entropy Function ◽  
Potential Well ◽  
Rapid Rise ◽  
Dimensional Model ◽  
One Dimensional ◽  
Spatial Entropy ◽  
Quantum Complexity ◽  
Entropy Growth ◽  
Infinite Potential Well

We use a one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of a locally defined spatial entropy function defined by S=-\int |\Psi(x,t)|^2 \ln |\Psi(x,t)|^2 dx . We show that changing the square barrier by increasing the height or width of the barrier not only decreases the tunneling but also slows down the rapid rise of the entropy function, indicating that the locally defined entropy growth is an essentially quantum effect.

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.

scholarly journals Quantum Lenoir Engine with a Single Particle System in a One Dimensional Infinite Potential Well

POSITRON ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 81
Author(s):  
Yohanes Dwi Saputra
Keyword(s):  
Quantum System ◽  
Single Particle ◽  
Thermal Efficiency ◽  
Particle System ◽  
Ideal Gas ◽  
Working Fluid ◽  
Potential Well ◽  
One Dimensional ◽  
Infinite Potential Well ◽  
The Ideal

Lenoir engine based on the quantum system has been studied theoretically to increase the thermal efficiency of the ideal gas. The quantum system used is a single particle (as a working fluid instead of gas in a piston tube) in a one-dimensional infinite potential well with a wall that is free to move. The analogy of the appropriate variables between classical and quantum systems makes the three processes for the classical Lenoir engine applicable to the quantum system. The thermal efficiency of the quantum Lenoir engine is found to have the same formulation as the classical one. The higher heat capacity ratio in the quantum system increases the thermal efficiency of the quantum Lenoir engine by 56.29% over the classical version at the same compression ratio of 4.41.

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.

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

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

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