What object does the wave function describe?

TL;DR

This paper argues that the wave function in quantum mechanics describes a statistical ensemble of particles rather than individual particles, emphasizing the ensemble interpretation as fundamental and incompatible with the notion of wave functions representing single particles.

Contribution

It demonstrates that the wave function corresponds to a statistical ensemble, not an individual particle, and clarifies the implications for the interpretation of quantum mechanics.

Findings

Wave function describes a statistical ensemble of particles.

Classical limit h=0 leads to equations for classical particle ensembles.

Statistical interpretation follows from the linearity constraints of QM formalism.

Abstract

It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle <S>. This result follows from the fact that in the classical limit h=0 the Schroedinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an individual particle is incompatible with the quantum mechanics formalism. It is shown that the statistical interpretation of quantum mechanics is a corollary of the fact, that the QM formalism is the technique of the statistical ensemble description, restricted by constraints of the dynamic equation linearity.