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Determination of the Exact Eigenvalues and Eigenfunctions of a Class of Quantum Anharmonic Oscillators with Polynomial Potential Functions

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  • Amos Odoom
  • Francis T. Oduro
  • Kwaku Darkwah
  • Ishmael Takyi

Abstract

We determine the exact eigenvalues and eigenfunctions of a class of quantum anharmonic oscillator using a novel non perturbative approach. Our method which has already been applied to quantum harmonic oscillator incorporates the Gram Schmidt Orthogonalization process to generate separate even and odd eigenfunction sequences. For concreteness, we study a specific instance of a quantum anharmonic oscillator having a polynomial potential of order six. The general class of quantum anharmonic oscillators considered here are those characterized by certain polynomial functions with terms of even power.

Suggested Citation

  • Amos Odoom & Francis T. Oduro & Kwaku Darkwah & Ishmael Takyi, 2022. "Determination of the Exact Eigenvalues and Eigenfunctions of a Class of Quantum Anharmonic Oscillators with Polynomial Potential Functions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(1), pages 1-72, March.
    • Handle: RePEc:ibn:jmrjnl:v:14:y:2022:i:1:p:72
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    References listed on IDEAS

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    1. Francis T. Oduro & Amos Odoom, 2021. "A New Framework for the Determination of the Eigenvalues and Eigenfunctions of the Quantum Harmonic Oscillator," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 13(6), pages 1-20, December.
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      • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
      • Z0 - Other Special Topics - - General

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