Open AccessA New Framework for the Determination of the Eigenvalues and Eigenfunctions of the Quantum Harmonic Oscillator
Author(s) -
Francis T. Oduro,
Amos Odoom
Publication year - 2021
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v13n6p20
Subject(s) - eigenfunction , orthogonalization , mathematics , eigenvalues and eigenvectors , harmonic oscillator , hilbert space , quantum harmonic oscillator , schrödinger equation , mathematical analysis , quantum , harmonic , quantum mechanics , geometry , physics
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.