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European Journal of Physics, 2013, Volume 34 Number 5, P1175.
Wajdi Gaddah
Department of Physics, Faculty of Science, University of Tripoli, PO Box 84441, Tripoli, Libya. [email protected]
Abstract
In this paper, we present Lie’s method of using one-parameter groups of continuous transformations to find the exact solution to the Schrödinger equation for a particle confined in an equilateral triangle. A suitable Lie group transformation that leaves the Schrödinger equation in the complex-variable formulation invariant is determined by detection and then used to reduce the partial differential equation to an ordinary differential equation which admits the so-called group-invariant solution. This particular solution along with other symmetry transformations is used to generate the full solution that complies with Dirichlet boundary conditions. The eigenfunctions and eigenvalues obtained herein are in full agreement with those derived by other methods. Our approach has been presented in a simple manner in the hope that it will be beneficial at the undergraduate level.
© 2013 IOP Publishing Ltd
