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

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

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

Coupling of impurities in the one-dimensional rectangular well model

Physica ◽  
1964 ◽  
Vol 30 (12) ◽  
pp. 2180-2184 ◽  
Author(s):  
Frederik Kuliasko
Keyword(s):  
One Dimensional ◽  
Well Model ◽  
The One

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 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.

THE PARTIAL POTENTIAL ENERGY SURFACE AND SCATTERING RESONANCE STATE OF THE STATE-TO-STATE REACTION Br + HBr(v) → BrH(v′) + Br

2006 ◽  
Vol 05 (spec01) ◽  
pp. 307-316 ◽  
Author(s):  
HUAYANG WANG ◽  
XIAOMIN SUN ◽  
DACHENG FENG ◽  
ZHENGTING CAI
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Minimum Energy ◽  
Resonance State ◽  
Minimum Energy Path ◽  
Resonance States ◽  
One Dimensional ◽  
Well Model ◽  
The One

In this paper, the partial potential energy surface (PPESs) of the Br + HBr and Br - + HBr systems including the minimum energy path and the vibrational potential curves were constructed at MP2/6-311++G** level, based on the conception and constructing approach of the PPESs previously proposed. These results obtained from the PPESs were compared with those from the high resolved threshold photodetachment spectrum of the BrHBr - anion measured by Neumark et al., J Phys Chem94, 1377–1388, 1990. On the basis of the PPESs, the scattering resonance states of the Br + HBr (v) → BrH (v′) + Br state-to-state reaction were studied and the satisfactory results were obtained. Subsequently, we calculated the width and lifetime of the resonance states in this reaction by the one-dimensional square potential well model, and obtained some results consistent to the experiments.

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