More quantum centrifugal effect in rotating frame

¹ APC, Univ Paris Diderot, Sorbonne Paris Cité - 75205 Paris, France
² Centro Brasileiro de Pesquisas Físicas - 22290-180 Rio de Janeiro, RJ, Brazil
³ Instituto de Física, Universidade Federal do Rio de Janeiro - C.P. 68528, 21941-972, Rio de Janeiro, RJ, Brazil
⁴ Division of Science Policy and Capacity Building, UNESCO - 7/9 place de Fontenoy, 75007 Paris, France

Received: 20 May 2017
Accepted: 18 July 2017

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 Schrödinger 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.