A theorem about time evolution in the quantum mechanics

TL;DR

This paper proves a fundamental theorem about the behavior of probability amplitudes in quantum mechanics, showing they are either constant or change continuously over time under broad conditions.

Contribution

It establishes a general theorem characterizing the possible time evolution of probability amplitudes in quantum systems.

Findings

Probability amplitudes are either constant or continuously changing over time.

The theorem applies under broad conditions in quantum mechanics.

Provides a foundational understanding of quantum state evolution.

Abstract

Under broad conditions, we prove that the probability amplitudes in the quantum mechanics are either always constant in time or changing continuously in any interval of time.