Energy levels for a square well containingδ-function barriers on a Cantor set

1989 ◽  
Vol 39 (11) ◽  
pp. 6018-6021 ◽  
Author(s):  
W. D. Heiss ◽  
W.-H. Steeb
Keyword(s):  
Energy Levels ◽  
Cantor Set ◽  
Square Well

Perturbative calculation of energy levels for the Dirac equation with generalized momenta

2020 ◽  
Vol 35 (20) ◽  
pp. 2050106
Author(s):  
Marco Maceda ◽  
Jairo Villafuerte-Lara
Keyword(s):  
Dirac Equation ◽  
Uncertainty Principle ◽  
Energy Levels ◽  
Generalized Uncertainty Principle ◽  
Spatial Dimension ◽  
Three Dimensions ◽  
Minimum Length ◽  
Linear Potential ◽  
Perturbative Calculation ◽  
Square Well

We analyze a modified Dirac equation based on a noncommutative structure in phase space originating from a generalized uncertainty principle with a minimum length. The noncommutative structure induces generalized momenta and contributions to the energy levels of the standard Dirac equation. Applying techniques of perturbation theory, we find the lowest-order corrections to the energy levels and eigenfunctions of the Dirac equation in three dimensions for a spherically symmetric linear potential and for a square-well times triangular potential along one spatial dimension. We find that the corrections due to the noncommutative contributions may be of the same order as the relativistic ones, leading to an upper bound on the parameter fixing the minimum length induced by the generalized uncertainty principle.

scholarly journals SPONTANEOUS BREAKDOWN OF $\mathcal{PT}$ SYMMETRY IN THE SOLVABLE SQUARE-WELL MODEL

2001 ◽  
Vol 16 (35) ◽  
pp. 2273-2280 ◽  
Author(s):  
MILOSLAV ZNOJIL ◽  
GÉZA LÉVAI
Keyword(s):  
Energy Levels ◽  
Pt Symmetry ◽  
Complex Conjugate ◽  
Spontaneous Breakdown ◽  
Well Model ◽  
Square Well

Apparently, the energy levels merge and disappear in many [Formula: see text] symmetric models. This interpretation is incorrect: In square-well model we demonstrate how the doublets of states in question continue to exist at complex conjugate energies in the strongly non-Hermitian regime.

scholarly journals Quantum-mechanical Wave Equation for Two Particles of Spin 0

1975 ◽  
Vol 28 (5) ◽  
pp. 495 ◽  
Author(s):  
Kwong-Chuen Tam
Keyword(s):  
Wave Equation ◽  
Hydrogen Atom ◽  
Coulomb Interaction ◽  
Energy Levels ◽  
Hamiltonian Formalism ◽  
Quantum Mechanical ◽  
Coulomb Interactions ◽  
Mechanical Wave ◽  
Square Well

A quantum-mechanical wave equation for two particles of spin 0 is presented in Hamiltonian formalism and is then simplified and discussed. Solutions are found for square-well and Coulomb interactions, and energy levels are determined. It is shown that, for the Coulomb interaction, the energy levels to the lowest order agree with those given by the hydrogen atom formula.

On the energy levels of a finite square-well potential

2000 ◽  
Vol 41 (7) ◽  
pp. 4551-4555 ◽  
Author(s):  
Prabasaj Paul ◽  
Daniel Nkemzi
Keyword(s):  
Energy Levels ◽  
Square Well

scholarly journals Tutorial: The quantum finite square well and the Lambert W function

2017 ◽  
Vol 95 (2) ◽  
pp. 105-110 ◽  
Author(s):  
Ken Roberts ◽  
S.R. Valluri
Keyword(s):  
Quantum Mechanics ◽  
Energy Levels ◽  
Inverse Image ◽  
Lambert W Function ◽  
Infrared Photodetector ◽  
Additional Insight ◽  
One Dimensional ◽  
Quantum Well Infrared Photodetector ◽  
Square Well ◽  
Insight Into

We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping w → z = wew between two complex domains. The solution of the finite square well problem can be seen to be described by the images of simple geometric shapes, lines, and circles, under this map and its inverse image. The technique can also be described using the Lambert W function. One can work in either of the complex domains, thereby obtaining additional insight into the finite square well problem and its bound energy states. This suggests interesting possibilities for the design of materials that are sensitive to minute changes in their environment such as nanostructures and the quantum well infrared photodetector.

RESONANCES ATTACHED TO THE SINGULARITIES OF THE FUNCTION COUPLING TWO SIMPLE SYSTEMS TO A FIELD

2008 ◽  
Vol 23 (07) ◽  
pp. 1039-1054 ◽  
Author(s):  
CLAUDE BILLIONNET
Keyword(s):  
Energy Levels ◽  
Free Field ◽  
Finite Depth ◽  
Wave Functions ◽  
Compton Wavelength ◽  
Two Systems ◽  
Whole Space ◽  
Square Well ◽  
Simple Systems ◽  
The Way

We examine resonances for two systems consisting of a particle coupled to a massless boson's field. The field is the free field in the whole space. In the first system, the particle is confined inside a ball. We show that besides the usual energy levels of the particle, which have become complex through the coupling to the field, other resonances are to be taken into account if the ball's radius is comparable to the particle's Compton wavelength. In the second system, the particle is in a finite-depth square-well potential. We study the way the resonances' energy and width depend on the extent of the uncoupled particle's wave functions. In both cases, we limit ourselves to considering two levels of the particle only.

Path representations of the quantum-mechanical energy-level density

1968 ◽  
Vol 64 (3) ◽  
pp. 787-794 ◽  
Author(s):  
Viktor Bezák
Keyword(s):  
Energy Level ◽  
Mechanical Energy ◽  
Level Density ◽  
Energy Levels ◽  
Partial Sums ◽  
Quantum Mechanical ◽  
Different Types ◽  
Square Well ◽  
The One ◽  
Quantum Mechanical Energy

AbstractThe quantum-mechanical energy-level density g(E) is given as a functional of the quantum-mechanical kernel K(q″, q′, t″ −t′). On taking the kernel K in the Feynman's form, one obtains the function g(E), without solving a Schrödinger equation. As an example, the embedding of a particle in the one-dimensional square well with infinitely high walls is analysed. The functions K(x″, x′, t−t′) and g(E) are represented as sums of terms corresponding to classical paths of different types. By an adequate choice of some terms due to the ‘most important’ paths, one may construct partial sums giving approximations of the function g(E). The utilization of such approximations for estimation of energy levels is demonstrated.

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