scholarly journals The one dimensional infinite square well with variable mass

2014 ◽  
Vol 8 ◽  
pp. 4285-4300
Author(s):  
J.J. Alvarez ◽  
M. Gadella ◽  
L.P. Lara
Keyword(s):  
Variable Mass ◽  
One Dimensional ◽  
Square Well ◽  
The One

scholarly journals A numerical test of a high-penetrability approximation for the one-dimensional penetrable-square-well model

2010 ◽  
Vol 133 (2) ◽  
pp. 024101 ◽  
Author(s):  
Riccardo Fantoni ◽  
Achille Giacometti ◽  
Alexandr Malijevský ◽  
Andrés Santos
Keyword(s):  
Numerical Test ◽  
One Dimensional ◽  
Well Model ◽  
Square Well ◽  
The One

scholarly journals ONE-DIMENSIONAL QUASI-RELATIVISTIC PARTICLE IN THE BOX

2013 ◽  
Vol 25 (08) ◽  
pp. 1350014 ◽  
Author(s):  
KAMIL KALETA ◽  
MATEUSZ KWAŚNICKI ◽  
JACEK MAŁECKI
Keyword(s):  
Relativistic Particle ◽  
Massive Particle ◽  
Relativistic Model ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Special Cases ◽  
Klein Gordon ◽  
Square Well ◽  
The One ◽  
Root Operator

The eigenvalues and eigenfunctions of the one-dimensional quasi-relativistic Hamiltonian (-ℏ2c2d2/dx2 + m2c4)1/2 + V well (x) (the Klein–Gordon square-root operator with electrostatic potential) with the infinite square well potential V well (x) are studied. Eigenvalues represent energies of a "massive particle in the box" quasi-relativistic model. Approximations to eigenvalues λn are given, uniformly in n, ℏ, m, c and a, with error less than C1ℏca-1 exp (-C2ℏ-1mca)n-1. Here 2a is the width of the potential well. As a consequence, the spectrum is simple and the nth eigenvalue is equal to (nπ/2 - π/8)ℏc/a + O(1/n) as n → ∞. Non-relativistic, zero mass and semi-classical asymptotic expansions are included as special cases. In the final part, some L2 and L∞ properties of eigenfunctions are studied.

scholarly journals Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 350
Author(s):  
Manuel Gadella ◽  
José Hernández-Muñoz ◽  
Luis Miguel Nieto ◽  
Carlos San Millán
Keyword(s):  
Ground State ◽  
Infinite Sequence ◽  
Negative Energy ◽  
Transcendental Equation ◽  
The Self ◽  
Positive Energy ◽  
One Dimensional ◽  
Square Well ◽  
The One ◽  
Adjoint Operators

We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator −d2/dx2 on L2[−a,a], a>0, that is, the one dimensional infinite square well. First of all, we classify these self-adjoint extensions in terms of several choices of the parameters determining each of the extensions. There are essentially two big groups of extensions. In one, the ground state has strictly positive energy. On the other, either the ground state has zero or negative energy. In the present paper, we show that each of the extensions belonging to the first group (energy of ground state strictly positive) has an infinite sequence of supersymmetric partners, such that the ℓ-th order partner differs in one energy level from both the (ℓ−1)-th and the (ℓ+1)-th order partners. In general, the eigenvalues for each of the self-adjoint extensions of −d2/dx2 come from a transcendental equation and are all infinite. For the case under our study, we determine the eigenvalues, which are also infinite, all the extensions have a purely discrete spectrum, and their respective eigenfunctions for all of its ℓ-th supersymmetric partners of each extension.

Condensation of gases on metals: The one-dimensional square well model

1973 ◽  
Vol 12 (6) ◽  
pp. v
Author(s):  
Ch. Steinbrüchel ◽  
L.D. Schmidt
Keyword(s):  
One Dimensional ◽  
Well Model ◽  
Square Well ◽  
The One

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

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