Chakraborty, S ; Bhattacharjee, J K ; Khastgir, S P (2009) An eigenvalue problem in two dimensions for an irregular boundary Journal of Physics A: Mathematical and Theoretical, 42 (19). p. 195301. ISSN 1751-8113
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Official URL: http://doi.org/10.1088/1751-8113/42/19/195301
Related URL: http://dx.doi.org/10.1088/1751-8113/42/19/195301
Abstract
An analytical perturbative method is suggested for solving the Helmholtz equation (∇2 + k2)ψ = 0 in two dimensions where ψ vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Institute of Physics Publishing. |
| ID Code: | 133881 |
| Deposited On: | 30 Dec 2022 11:59 |
| Last Modified: | 30 Dec 2022 11:59 |
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