arXiv:physics/0501012

Approximation of the energy levels of the particle on a segment by energy levels of the particle in monomial potential well

Michal Demetrian

Published Jan 4, 2005• 0 citations

Abstract

This simple text considers an application of Bohr-Sommerfeld quantization rule. It might be of interest for the students of physics.

DOI: 10.48550/arxiv.physics/0501012

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arXiv:physics/0501012

Approximation of the energy levels of the particle on a segment by energy levels of the particle in monomial potential well

Michal Demetrian

Published Jan 4, 2005• 0 citations

arXiv HTML PDF

Abstract

This simple text considers an application of Bohr-Sommerfeld quantization rule. It might be of interest for the students of physics.

DOI: 10.48550/arxiv.physics/0501012

Related papers

Generalization of the Bohr-Sommerfeld Quantization Rule and its Application to Quantum Tunneling

WORLD SCIENTIFIC eBooksJan 1, 20030 citations

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WORLD SCIENTIFIC eBooksJan 14, 20141 citation

A new approach to bound states in potential wells

Jean‐Francis Bloch, V. K. Ignatovich

A method for calculating the energies of the bound states of a particle in a potential well is presented. A generalization of the Bohr–Sommerfeld quantization rule is obtained.

American Journal of PhysicsNov 1, 20017 citations

Bohr–Sommerfeld, WKB, and modified semiclassical quantization rules

D. J. W. Geldart, David Kiang

American Journal of PhysicsFeb 1, 198611 citations

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MA Er-ju

College PhysicsJan 1, 20140 citations

Bohr–Sommerfeld Quantization Rule in the Case of a Two-Dimensional Motion of a Quantum Particle in the Field of Decreasing Power-Like Potential

Vasily Veniaminovitch Pupyshev

We study the finite two-dimensional motion of a quantum particle in the field of the potential $V(r) = - {{V}_{0}}{{r}^{{ - \beta }}}$ with parameters ${{V}_{0}} > 0$ and $\beta \in (0,2)$ . An analysis of an asymptotic equation equivalent to the Bohr–Sommerfeld quantization rule is given. As a result, a simple and explicit approximation for the energies of weakly-bound states of this particle has been obtained.We study the finite two-dimensional motion of a quantum particle in the field of the potential $$V(r) = - {{V}_{0}}{{r}^{{ - \beta }}}$$ with parameters $${{V}_{0}} > 0$$ and $$\beta \in (0,2)$$ . An analysis of an asymptotic equation equivalent to the Bohr–Sommerfeld quantization rule is given. As a result, a simple and explicit approximation for the energies of weakly-bound states of this particle has been obtained.

Physics of Particles and NucleiJul 1, 20201 citation

We study the finite two-dimensional motion of a quantum particle in the field of the potential

V(r) = - {{V}_{0}}{{r}^{{ - \beta }}}

with parameters

{{V}_{0}} > 0

and

\beta \in (0,2)

. An analysis of an asymptotic equation equivalent to the Bohr–Sommerfeld quantization rule is given. As a result, a simple and explicit approximation for the energies of weakly-bound states of this particle has been obtained.