Physics – Mathematical Physics
Scientific paper
2010-04-12
Physics
Mathematical Physics
25 pages, no figures
Scientific paper
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we find two equivalent pictures: a constrained local description in position containing additional degrees of freedom, and an unconstrained nonlocal description in terms of the position without any other degrees of freedom. Both these descriptions have a corresponding classical theory which shows that the concept of extended, structured objects emerges quite naturally and unavoidably there. It is explicitly demonstrated that the conserved energy and angular momentum contain corrections to those of a point particle. We argue that these notions also extend naturally to the quantum level. The local description is found to be the most convenient as it manifestly displays additional information about structure of quantum states that is more subtly encoded in the nonlocal, unconstrained description. Subsequently we use this picture to discuss the free particle and harmonic oscillator as examples.
Gouba Laure
Rohwer C. M.
Scholtz Frederik G.
Zloshchastiev Konstantin G.
No associations
LandOfFree
Noncommutative quantum mechanics -- a perspective on structure and spatial extent does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Noncommutative quantum mechanics -- a perspective on structure and spatial extent, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noncommutative quantum mechanics -- a perspective on structure and spatial extent will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-263046