Wave Functions for Anharmonic Oscillators by Perturbation Methods

1962 ◽  
Vol 37 (5) ◽  
pp. 1043-1055 ◽  
Author(s):  
A. M. Shorb ◽  
R. Schroeder ◽  
E. R. Lippincott
Keyword(s):  
Perturbation Methods ◽  
Wave Functions ◽  
Anharmonic Oscillators

Energetics, wave functions, and spectroscopy of coupled anharmonic oscillators

1983 ◽  
Vol 78 (3) ◽  
pp. 1348-1358 ◽  
Author(s):  
Martin L. Sage ◽  
J. A. Williams
Keyword(s):  
Wave Functions ◽  
Anharmonic Oscillators

On the relationship between anharmonic oscillators and perturbed Coulomb potentials in N dimensions

2000 ◽  
Vol 77 (11) ◽  
pp. 863-871 ◽  
Author(s):  
D A Morales ◽  
Z Parra-Mejías
Keyword(s):  
Exact Solutions ◽  
Ground State ◽  
Free Parameter ◽  
Anharmonic Oscillator ◽  
Wave Functions ◽  
Anharmonic Oscillators ◽  
Supersymmetric Partner ◽  
The Relationship ◽  
Coulomb Potentials ◽  
03.65 Ge

The relation between the perturbed Coulomb problem in N dimensionsand the sextic anharmonic oscillator in N' dimensionsis presented and generalized in this work.We show that by performing a transformation, containing a free parameter, on the equations for the two problems we can relate the two systems in dimensions that have not been previously linked. Exact solutions can be obtained for the N-dimensional systems from knownthree-dimensional solutions of the two problems. Using the known ground-state wave functions for these systems, we construct supersymmetric partner potentials that allow us to apply the supersymmetric large-Nexpansion to obtain accurate approximate energy eigenvalues.PACS Nos.: 03.65.Ge, 03.65.Fd, 11.30.Na

Perturbation and variational-perturbation method for the free energy of anharmonic oscillators

2007 ◽  
Vol 85 (1) ◽  
pp. 13-30 ◽  
Author(s):  
K Vlachos ◽  
V Papatheou ◽  
A Okopińska
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Perturbation Method ◽  
Perturbation Methods ◽  
Anharmonic Oscillator ◽  
Numerical Calculations ◽  
Anharmonic Oscillators ◽  
One Dimensional ◽  
Variational Perturbation ◽  
Fifth Order

The perturbation and the variational-perturbation methods are applied for calculating the partition function of one-dimensional oscillators with anharmonicity x2n. New formally simple expressions for the free energy and for the Rayleigh–Schrodinger energy corrections are derived. It is shown that the variational-perturbation method overcomes all the deficiencies of the conventional perturbation method. The results of fifth-order numerical calculations for the free energy of the quartic, quartic–sextic, and octic anharmonic oscillator are highly accurate in the whole range of temperatures. PACS Nos.: 03.65.–w, 05.30.–d

Magnetotunneling spectroscopy imaging of electron wave functions in self-assembled InAs quantum dots

2001 ◽  
Vol 171 (12) ◽  
pp. 1365
Author(s):  
E.E. Vdovin ◽  
Yu.N. Khanin ◽  
Yu.V. Dubrovskii ◽  
A. Veretennikov ◽  
A. Levin ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Wave Functions ◽  
Electron Wave ◽  
Inas Quantum Dots ◽  
Self Assembled

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

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