scholarly journals Quantum square-well with logarithmic central spike

2018 ◽  
Vol 33 (02) ◽  
pp. 1850009 ◽  
Author(s):  
Miloslav Znojil ◽  
Iveta Semorádová
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Closed Form ◽  
Wave Functions ◽  
Change Of Variables ◽  
State Dependent ◽  
Square Well ◽  
Strength Formula ◽  
Schrödinger Perturbation ◽  
Dependent Interaction

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

APPROXIMATE MOLECULAR ORBITALS: III. THE 1sσ AND 2pπ STATES OF HeH++

1967 ◽  
Vol 45 (7) ◽  
pp. 2231-2238 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran ◽  
Sheila D. McPhee
Keyword(s):  
Perturbation Theory ◽  
Molecular Orbitals ◽  
Wave Functions ◽  
Variational Techniques ◽  
Approximate Wave ◽  
Schrödinger Perturbation

A combination of Rayleigh–Schrödinger perturbation theory and variational techniques, previously used to calculate the wave functions of the lowest σ and π states of H2+ has been applied to the 1sσ and 2pπ states of HeH++. The accuracy of the resulting approximate wave functions is demonstrated by comparing a number of quantities calculated with them with the corresponding exact values.

APPROXIMATE MOLECULAR ORBITALS: IV. THE 3dδg AND 4fδu STATES OF H2+

1967 ◽  
Vol 45 (8) ◽  
pp. 2533-2542 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran ◽  
Sheila D. McPhee
Keyword(s):  
Perturbation Theory ◽  
Variational Methods ◽  
Excellent Agreement ◽  
Hydrogen Molecule ◽  
Wave Functions ◽  
Simple Criterion ◽  
Wide Range ◽  
Approximate Wave ◽  
Exact Calculations ◽  
Schrödinger Perturbation

Properties of the lowest even and odd δ states of the hydrogen molecule–ion have been calculated using approximate wave functions. These were derived using a combination of Rayleigh–Schrödinger perturbation theory and variational methods, which have been applied previously to calculate the corresponding wave functions of the lowest σ and π states. Our total molecular energies are in excellent agreement with the recent exact calculations of Hunter and Pritchard (1967). A simple criterion is suggested for judging the accuracy of the approximate orbitals, which indicates that all the molecular properties calculated will be accurate over a wide range of internuclear separations.

Closed-form rectangular atomic wave functions of anN-dimensional atom

2002 ◽  
Vol 88 (2) ◽  
pp. 263-274 ◽  
Author(s):  
Shun S. Lo ◽  
Daniel A. Morales
Keyword(s):  
Closed Form ◽  
Wave Functions ◽  
Atomic Wave

Applicability of the schrödinger perturbation theory to bound states

1964 ◽  
Vol 10 (1) ◽  
pp. 73 ◽  
Author(s):  
K. Hausmann ◽  
W. Macke ◽  
P. Ziesche
Keyword(s):  
Perturbation Theory ◽  
Bound States ◽  
Schrödinger Perturbation

scholarly journals A full wave description for thin wire structures with TLST and perturbation theory

2018 ◽  
Vol 16 ◽  
pp. 123-133
Author(s):  
Fabian Ossevorth ◽  
Ralf T. Jacobs ◽  
Hans Georg Krauthäuser
Keyword(s):  
Perturbation Theory ◽  
Closed Form ◽  
Current Distribution ◽  
Perturbation Approach ◽  
Mixed Potential ◽  
Thin Wire ◽  
Method Of Moment ◽  
Initial Current ◽  
Full Wave ◽  
Good Agreement

Abstract. A full wave description of a thin wire structure, that includes mutual interactions and radiation, can be obtained in closed form with the so-called Transmission Line Super Theory or a refined variant of this method that utilises perturbation theory. In either procedure, a set of mixed potential integral equations is solved for the currents that propagate along a wire. With the perturbation approach, no iteration is required to approximate the initial current distribution on the wire. This procedure will be applied to solve multi-wire problems. The theory will be derived and computed results will be shown to be in good agreement with method of moment computations.

scholarly journals Influence of the Parameterization in the Interval Solution of Elastic Beams

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Stefano Gabriele ◽  
Valerio Varano
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Interval Analysis ◽  
Elastic Beam ◽  
Elastic Beams ◽  
Analysis Theory ◽  
Set Intersection ◽  
Interval Solution ◽  
Uncertain Boundary

We are going to analyze the interval solution of an elastic beam under uncertain boundary conditions. Boundary conditions are defined as rotational springs presenting interval stiffness. Developments occur according to the interval analysis theory, which is affected, at the same time, by the overestimation of interval limits (also known as overbounding, because of the propagation of the uncertainty in the model). We suggest a method which aims to reduce such an overestimation in the uncertain solution. This method consists in a reparameterization of the closed form Euler-Bernoulli solution and set intersection.

Sign in / Sign up

Export Citation Format

Share Document