A note on function spaces spanned by complex energy eigenfunctions

Kunio Miyoshi, Masayoshi Suzaki

A. J. van Wonderen, K. Lendi

The standard representation of angular momentum on Bargmann's Hilbert space of analytic functions is extended such that domains of operators include non-analytic functions, which are square integrable. Generalized eigenfunctions of angular momentum are proposed, which contain arbitrary complex constants. The eigenfunctions are shown to satisfy a basic requirement which follows from group theory.

Rainer Dick

Rainer Dick

Mehdi Hage-Hassan

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.

Rainer Dick