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A New Framework for the Determination of the Eigenvalues and Eigenfunctions of the Quantum Harmonic Oscillator

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  • Francis T. Oduro
  • Amos Odoom

Abstract

This study was designed to obtain the energy eigenvalues and the corresponding Eigenfunctions of the Quantum Harmonic oscillator through an alternative approach. Starting with an appropriate family of solutions to a relevant linear di erential equation, we recover the Schr¨odinger Equation together with its eigenvalues and eigenfunctions of the Quantum Harmonic Oscillator via the use of Gram Schmidt orthogonalization process in the usual Hilbert space. Significantly, it was found that there exists two separate sequences arising from the Gram Schmidt Orthogonalization process; one in respect of the even eigenfunctions and the other in respect of the odd eigenfunctions.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:jmrjnl:v:13:y:2021:i:6:p:20
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    Cited by:

    1. 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.

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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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