Anharmonic oscillator via Legendre and Chebyshev pseudo-spectral methods

Anharmonic oscillator via Legendre and Chebyshev pseudo-spectral methods


  • ˙ Inci M. Erhan, Saeida M. Wlie


Schr¨odinger equation, pseudospectral method, Chebyshev polynomial, Legendre polynomial


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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How to Cite

Anharmonic oscillator via Legendre and Chebyshev pseudo-spectral methods. (2023). Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 66-80.