Anharmonic oscillator via Legendre and Chebyshev pseudo-spectral methods
Keywords:
Schr¨odinger equation, pseudospectral method, Chebyshev polynomial, Legendre polynomialAbstract
In this study, we introduce the pseudospectral methods based on Chebyshev and Legendre polynomials for the Schr¨odinger equation of anharmonic oscillator. The method transforms the problem into an unsymmetric matrix eigenvalue problem which can be symmetrized by using a suitable similarity transformation. Computation of the zeros of the relevant orthogonal polynomials is also converted into a symmetric matrix eigenvalue problem. The method is applied to the Scr¨odinger equation of an anharmonic oscillator of various types and the numerical results and discussed.
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