The energy levels of the one‐dimensional potential well V (X) =a‖X‖ calculated by means of certain phase‐integral approximations

1976 ◽  
Vol 17 (7) ◽  
pp. 1222-1225 ◽  
Author(s):  
Bo Thidé
Keyword(s):  
Energy Levels ◽  
Potential Well ◽  
One Dimensional ◽  
Phase Integral ◽  
The One

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

scholarly journals Spectral Statistics of the Triaxial Rigid Rotator: Semiclassical Origin of Their Pathological Behavior

2003 ◽  
Vol 17 (15) ◽  
pp. 803-812
Author(s):  
V. R. Manfredi ◽  
V. Penna ◽  
L. Salasnich
Keyword(s):  
Angular Momentum ◽  
Spectral Properties ◽  
Total Angular Momentum ◽  
Energy Levels ◽  
Rigid Rotator ◽  
One Dimensional ◽  
Spectral Statistics ◽  
Rotational Motions ◽  
Pathological Behavior ◽  
The One

In this paper we investigate the local and global spectral properties of the triaxial rigid rotator. We demonstrate that, for a fixed value of the total angular momentum, the energy spectrum can be divided into two sets of energy levels, whose classical analogs are librational and rotational motions. By using diagonalization, semiclassical and algebric methods, we show that the energy levels follow the anomalous spectral statistics of the one-dimensional harmonic oscillator.

scholarly journals ON THE SPECTRUM OF THE ONE-DIMENSIONAL SCHRÖDINGER HAMILTONIAN PERTURBED BY AN ATTRACTIVE GAUSSIAN POTENTIAL

2017 ◽  
Vol 57 (6) ◽  
pp. 385 ◽  
Author(s):  
Silvestro Fassari ◽  
Manuel Gadella ◽  
Luis Miguel Nieto ◽  
Fabio Rinaldi
Keyword(s):  
Discrete Spectrum ◽  
Energy Levels ◽  
Trace Class ◽  
Bound State ◽  
Great Accuracy ◽  
Coupling Constant ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Gaussian Potential ◽  
The One

<p>We propose a new approach to the problem of finding the eigenvalues (energy levels) in the discrete spectrum of the one-dimensional Hamiltonian with an attractive Gaussian potential by using the well-known Birman-Schwinger technique. However, in place of the Birman-Schwinger integral operator we consider an isospectral operator in momentum space, taking advantage of the unique feature of this potential, that is to say its invariance under Fourier transform. <br />Given that such integral operators are trace class, it is possible to determine the energy levels in the discrete spectrum of the Hamiltonian as functions of <span>the coupling constant with great accuracy by solving a finite number of transcendental equations. We also address the important issue of the coupling constant thresholds of the Hamiltonian, that is to say the critical values of λ for which we have the emergence of an additional bound state out of the absolutely continuous spectrum. </span></p>

scholarly journals Exact Green's Function for the Finite Rectangular Potential Well in One Dimension

1985 ◽  
Vol 40 (4) ◽  
pp. 379-382 ◽  
Author(s):  
R. Baltin
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Free Particle ◽  
One Dimension ◽  
Potential Well ◽  
Complex Energy ◽  
One Dimensional ◽  
Special Cases ◽  
The One ◽  
Energy Plane

For the one-dimensional potential well with finite height V0( V0 > 0 or V0 < 0) the exact Green's function G is calculated by solving the differential equation. The poles of G in the complex energy plane are shown to coincide with the solutions to the Schrödinger eigenvalue equation for this potential. The well-known Green's functions for the special cases of the free particle and of the particle in an infinitely high potential box are recovered.

scholarly journals Equilibrium Charge Distribution in a Finite Chain with a Trapping Site

2021 ◽  
Vol 16 (1) ◽  
pp. 152-168
Author(s):  
N.S. Fialko ◽  
M.M. Olshevets ◽  
V.D. Lakhno
Keyword(s):  
Quantum Particle ◽  
Potential Well ◽  
Finite Chain ◽  
Polaron Model ◽  
One Dimensional ◽  
Equilibrium Charge ◽  
Direct Modeling ◽  
A Chain ◽  
The One ◽  
Charge Transfer In Dna

The paper considers the problem of the distribution of a quantum particle in a classical one-dimensional lattice with a potential well. The cases of a rigid chain, a Holstein polaron model, and a polaron in a chain with temperature are investigated by direct modeling at fixed parameters. As is known, in the one-dimensional case, a particle is captured by an arbitrarily shallow potential well with an increase of the box size. In the case of a finite chain and finite temperatures, we have quite the opposite result, when a particle, being captured in a well in a short chain, turns into delocalized state with an increase in the chain length. These results may be helpful for further understanding of charge transfer in DNA, where oxoguanine can be considered as a potential well in the case of hole transfer when for excess electron transfer it is thymine dimer.

Ocean Acoustics

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Mathematical Model ◽  
Velocity Structure ◽  
Potential Well ◽  
Ocean Acoustics ◽  
Underwater Sound ◽  
Acoustic Wave Propagation ◽  
One Dimensional ◽  
Acoustic Waveguides ◽  
Water Transmission ◽  
The One

This chapter deals with the mathematics of ocean acoustics. A number of environmental factors affect the transmission of sound in the ocean, including the depth and configuration of the bottom, the sound velocity structure within the ocean, and the shape of the ocean surface. The depths in the ocean are distributed in a peculiar manner, and the solution of underwater-sound problems may be grouped into two categories that differ mainly in terms of dimension: the average depths of water for deep-water transmission are 10,000 to 20,000 feet, whereas those for shallow-water transmission are less than 300 feet. The chapter first provides an overview of ocean acoustic waveguides before discussing one-dimensional waves in an inhomogeneous medium. It also considers a mathematical model of acoustic wave propagation in a stratified fluid and concludes with an analysis of the one-dimensional time-independent Schrödinger equation for solving the potential well problem.

scholarly journals Perturbation of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier

2020 ◽  
Vol 18 (1) ◽  
pp. 1413-1422
Author(s):  
Soon-Mo Jung ◽  
Ginkyu Choi
Keyword(s):  
Schrödinger Equation ◽  
Potential Barrier ◽  
Schrodinger Equation ◽  
Applied Mathematics ◽  
Finite Depth ◽  
Ulam Stability ◽  
Potential Well ◽  
One Dimensional ◽  
The One ◽  
Continuous Work

Abstract In Applied Mathematics Letters 74 (2017), 147–153, the Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation was investigated when the relevant system has a potential well of finite depth. As a continuous work, we prove in this paper a type of Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier of {V}_{0} in height and 2c in width, where {V}_{0} is assumed to be greater than the energy E of the particle under consideration.

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