The stationary states of the quantum harmonic oscillator are properly determined by means of the unilateral Fourier transform without having to recourse to the properties of the confluent hypergeometric functions. This simpler procedure is reminiscent of the algebraic method based on the ladder operators and depends on the value of just one tabulated definite integral related to the ground state.
Keywords:
Fourier transform; Harmonic oscillator; Unilateral Fourier transform