Physics – Mathematical Physics
Scientific paper
2008-12-16
J. Phys. A: Math. Theor. 42 (2009) 195301
Physics
Mathematical Physics
16 pages, 4 figures, v2 matches the journal version
Scientific paper
An analytical perturbative method is suggested for solving the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions where {\psi} 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.
Bhattacharjee Jayant K.
Chakraborty Subhasish
Khastgir Pratik S.
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