Barrier escape from a truncated quartic potential driven by correlated Lévy noises with opposite correlation

Abstract A potential energy function is proposed which exhibits a quartic dependence on (r - re), where re is the equilibrium interparticle distance, in the neighbourhood of re, and has a finite binding energy. To study the pattern of the eigenvalues, the WKBJ method is applied to the third order, and the relevant integrals are evaluated analytically. Results are shown graphically for a few sets of parameters. The number of vibrational states that the potential can support is determined for a range of values of the parameters. Some suggestions as to the possible applications of the proposed potential are also made.

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The quartic potential: instantons

Path Integrals and Hamiltonians ◽

10.1017/cbo9780511842450.018 ◽

2014 ◽

pp. 351-384

Author(s):

Belal E. Baaquie

Keyword(s):

Quartic Potential

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Exact solutions of a quartic potential

Modern Physics Letters A ◽

10.1142/s0217732319502080 ◽

2019 ◽

Vol 34 (26) ◽

pp. 1950208 ◽

Cited By ~ 6

Author(s):

Qian Dong ◽

Guo-Hua Sun ◽

M. Avila Aoki ◽

Chang-Yuan Chen ◽

Shi-Hai Dong

Keyword(s):

Exact Solutions ◽

Quantum System ◽

Analytical Solutions ◽

Wave Functions ◽

Negative Potential ◽

Potential Parameter ◽

Real Numbers ◽

Quartic Potential ◽

Heun Functions ◽

Potential Parameters

We find that the analytical solutions to quantum system with a quartic potential [Formula: see text] (arbitrary [Formula: see text] and [Formula: see text] are real numbers) are given by the triconfluent Heun functions [Formula: see text]. The properties of the wave functions, which are strongly relevant for the potential parameters [Formula: see text] and [Formula: see text], are illustrated. It is shown that the wave functions are shrunk to the origin for a given [Formula: see text] when the potential parameter [Formula: see text] increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter [Formula: see text] increases or parameter [Formula: see text] decreases for a given negative potential parameter [Formula: see text]. The minimum value of the double well case ([Formula: see text]) is given by [Formula: see text] at [Formula: see text].

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On the integrability of the Calogero-Moser system in an external quartic potential and other many-body systems

Physics Letters A ◽

10.1016/0375-9601(84)90784-9 ◽

1984 ◽

Vol 102 (3) ◽

pp. 85-88 ◽

Cited By ~ 16

Author(s):

Stefan Wojciechowski

Keyword(s):

Many Body ◽

Quartic Potential ◽

Many Body Systems ◽

Moser System

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NEW METHOD FOR SCHRÖDINGER EIGENVALUE PROBLEM — The Case of the Potential V(x) = 2μx2 + λx4

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194512008045 ◽

2012 ◽

Vol 17 ◽

pp. 149-158

Author(s):

TORU NAKAMURA ◽

HIROSHI EZAWA ◽

KEIJI WATANABE ◽

TOSHIHARU IRISAWA

Keyword(s):

Eigenvalue Problem ◽

Iteration Procedure ◽

Divergent Series ◽

New Method ◽

Wkb Method ◽

Quartic Potential

A new method is proposed to solve the Schrödinger eigenvalue problem. Remarkably the iteration procedure is found to be convergent in the case of the quartic potential for which the perturbation and the WKB method are known to give divergent series.

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