# More quantum centrifugal effect in rotating frame

## TL;DR

This paper uses affine coherent state quantization to analyze quantum particles in a rotating frame, revealing an additional quantum centrifugal effect that prevents particles from reaching the rotation center and explaining previous non-inertial Schrödinger equations.

## Contribution

It introduces a new quantum centrifugal term via ACS quantization, enhancing understanding of quantum behavior in rotating frames and clarifying earlier theoretical discrepancies.

## Key findings

- Prediction of an extra quantum centrifugal barrier.
- Explanation of two different non-inertial Schrödinger equations.
- Potential experimental verification through harmonic oscillator states.

## Abstract

The behaviour of quantum systems in non-inertial frames is revisited from the point of view of affine coherent state (ACS) quantization. We restrict our approach to the one-particle dynamics confined in a rotating plane about a fixed axis. This plane is considered as punctured due to the existence of the rotation center, which is viewed as a singularity. The corresponding phase space is the affine group of the plane and the ACS quantization enables us to quantize the system by respecting the affine symmetry of the true phase space. Our formulation predicts the appearance of an additional quantum centrifugal term, besides the usual angular momentum one, which prevents the particle to reach the singular rotation center. Moreover it helps us to understand why two different non-inertial Schr\"{o}dinger equations are obtained in previous works. The validity of our equation can be confirmed experimentally by observing the harmonic oscillator bound states and the critical angular velocity for their existence.