Abstract
The states of linear momentum that satisfy the equality in the Heisenberg uncertainty principle for position and momentum, that is the intelligent states, are also the states that minimize the uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the constrained minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the constrained minimum uncertainty product states for the angular case by means of instructive approximations, a numerical iterative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.
Highlights
Is that, unlike the linear position, the angular position takes values only over a finite range of size 2π
We find that the difference in uncertainty product between intelligent and constrained minimum uncertainty product (CMUP) states should be measurable with present technology
In this paper we have examined the states that minimize the uncertainty product of angular position and angular momentum either for a given variance in angle or for a given variance in angular momentum
Summary
Expressing the expectation value of this operator in terms of the angle wavefunction ψ(φ) that is normalized in a 2π interval, allows us to write the corresponding uncertainty relation as. The angular uncertainty relation (4) is of particular interest because it is an example of a case where the intelligent states, which satisfy the equality, do not necessarily minimize the uncertainty product on the left-hand side. This is because the second term on the right-hand side is itself state-dependent. The state exp(iφk)|g will be an intelligent state with a non-zero mean angular momentum
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
