Solution of the harmonic oscillator equation has a goal to get the energy levels of particles moving harmonic. The energy spectrums of one dimensional harmonic oscillator are analyzed by 3 methods: path integral, hypergeometry and operator. Analysis of the energy spectrum by path integral method is examined with Schrodinger equation. Analysis of the energy spectrum by operator method is examined by Hamiltonian in operator. Analysis of harmonic oscillator energy by 3 methods: path integral, hypergeometry and operator are getting same results ???? = ℏ???? (???? + 1 2)
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