The SchrÖdinger equation in rotating frames by using the stochastic variational method

Abstract

We give a pedagogical introduction of the stochastic variational method by considering the quantization of a non-inertial particle system. We show that the effects of fictitious forces are represented in the forms of vector fields which behave analogous to the gauge fields in the electromagnetic interaction. We further discuss that the operator expressions for observables can be defined by applying the stochastic Noether theorem.

More quantum centrifugal effect in rotating frame

“…In Ref. [8], a stochastic generalization of the variational calculus is applied. Whatever the differences between these approaches, the obtained results are compatible.…”

“…Moreover, our formulation helps us to understand why we had two different non-inertial Schrödinger equations, Refs. [1,[4][5][6][7][8] and Ref. [9].…”

“…When we choose (N 0 , N 1 ) = (1, 1/2) so as to reproduce the results in Refs. [4][5][6][7][8] at the exception of the σ-term, Ω can be larger than the maximum value in the classical case and the critical value is given by Ω cri = √ 2ω. On the other hand, when we choose (N 0 , N 1 ) = (2, 1/2) to reproduce Ref.…”