Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls

Al-Hashimi, Munir H. (2013). Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls. Molecular Physics, 111(2), pp. 225-241. Taylor & Francis 10.1080/00268976.2012.716526

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We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Institute of Theoretical Physics
10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)

UniBE Contributor:

Al-Hashimi, Munir

Subjects:

500 Science > 530 Physics

ISSN:

1362-3028

Publisher:

Taylor & Francis

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

19 Jun 2014 10:22

Last Modified:

26 Oct 2015 09:10

Publisher DOI:

10.1080/00268976.2012.716526

BORIS DOI:

10.7892/boris.46306

URI:

https://boris.unibe.ch/id/eprint/46306

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