Normalized Observational Probabilities from Unnormalizable Quantum States or Phase-Space Distributions

TL;DR

This paper demonstrates that normalized observational probabilities can be derived from non-normalizable quantum states or phase-space distributions, challenging the assumption that such states must be normalizable.

Contribution

It introduces a method to extract meaningful probabilities from unnormalizable quantum states or phase-space distributions, expanding the theoretical framework of quantum probability.

Findings

Normalized probabilities can be obtained from unnormalizable states.

The approach applies to both quantum states and phase-space distributions.

Challenges the conventional requirement of normalizability in quantum theory.

Abstract

Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it.