A note on the normalization of the momentum eigenfunctions and Dirac delta function

Mehdi Hage-Hassan (1)

1 UL - Faculté des Sciences Section (1)

We determine the generating function of the harmonic oscillator by a new method. Using this generating function we derive the eigenfunctions of the moment p. We find that the normalization of these eigenfunctions is a real and not complex number with phase factor chosen equal one (standard books of quantum mechanics). We prove that the integral of the delta function is equal to one and we derive the oscillator propagator.

Mots clés: Harmonic oscillator; generating function; normalization of momentum eigenfunctions; delta function; oscillator propagator

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Mehdi Hage-Hassan. A note on the normalization of the momentum eigenfunctions and Dirac delta function. 2014. ⟨hal-00978136v2⟩