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Journal of Hunan University of Science and Engineering

The selection and application of a rotating reference frame

Xia Li

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

This paper expounds a general method for taking a rotating reference frame in quantum optics, and also gives a example to show it by taking a appropriate rotating reference frame. We can change the Hamiltonian of a system into a simpler form. further, we can simple the calculation and successfully solve a problem. Finally, we give a general conclusion for taking a rotating reference frame.

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This paper expounds a general method for taking a rotating reference frame in quantum optics, and also gives a example to show it by taking a appropriate rotating reference frame. We can change the Hamiltonian of a system into a simpler form. further, we can simple the calculation and successfully solve a problem. Finally, we give a general conclusion for taking a rotating reference frame.
In physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. We develop a framework for rotational (i.e., spin) quantum reference frames, with respect to which quantum systems with spin degrees of freedom are described. We give an explicit model for such frames as systems composed of three spin coherent states of angular momentum jjj and introduce the transformations between them by upgrading the Euler angles occurring in classical SO(3)\text{SO}(3)SO(3) spin transformations to quantum mechanical operators acting on the states of the reference frames. To ensure that an arbitrary rotation can be applied on the spin we take the limit of infinitely large jjj, in which case the angle operator possesses a continuous spectrum. We prove that rotationally invariant Hamiltonians (such as that of the Heisenberg model) are invariant under a larger group of quantum reference frame transformations. Our result is a development of the quantum reference frame formalism for a non-Abelian group.
Abstract In quantum mechanics courses, the concept of a reference frame is frequently hidden. In this article, we present a basic perspective to introduce the transformations of a reference frame based on unitary transformations. These unitary transformations are inspired in canonical transformation for reference frame from the perspective of classical mechanics. The manner we deal with this change in reference frame allows us to discuss some fundamental concepts in Schrödinger and Heisenberg pictures, as well as the ideas of passive and active description in quantum mechanics. These unitary transformations are inspired in a reference-frame canonical transformation from the perspective of classical mechanics. The approach we take for this reference-frame change allows for a discussion on fundamental concepts in Schrödinger and Heisenberg pictures, as well as the ideas of passive and active description in quantum mechanics. We apply this unitary transformation in five examples.
We consider the process of changing reference frames in the case where the reference frames are quantum systems. We find that, as part of this process, decoherence is necessarily induced on any quantum system described relative to these frames. We explore this process with examples involving reference frames for phase and orientation. Quantifying the effect of changing quantum reference frames provides a theoretical description for this process in quantum experiments, and serves as a first step in developing a relativity principle for theories in which all objects including reference frames are necessarily quantum.