Critical comments on quantization of the angular momentum: I. Analysis based on the physical requirement on eigenfunctions and on the commutation relations

TL;DR

This paper challenges traditional assumptions by showing that angular momentum eigenvalues can be non-integer, based on analysis of eigenfunctions and commutation relations, questioning the standard quantization rules.

Contribution

It demonstrates that normalizable eigenfunctions with non-integer eigenvalues are possible, questioning the conventional integer-only spectrum of angular momentum.

Findings

Eigenfunctions with non-integer eigenvalues are normalizable.

Standard commutation relations do not restrict eigenvalues to integers.

Non-integer angular momentum eigenvalues are theoretically admissible.

Abstract

Eigenfunctions and eigenvalues of the operator of the square of the angular momentum are studied. It is shown that neither from the requirement for the eigenfunctions be normalizable nor from the commutation relations it is possible to prove that the eigenvalues spectrum is a set of only integer numbers (in units $\hbar=1$). We present regular, normalizable eigenfunctions with the non-integer eigenvalues thus demonstrating that a non-integer angular momentum is admissible from the theoretical viewpoint.