Quantum Mechanics on discrete space and time

Details Quantum Mechanics on discrete space and time Quantum Mechanics on discrete space and time

2004-01-02

arxiv.org/abs/quant-ph/0401004v1

Physics

Quantum Physics

Proceedings: M. Ferrero, A. van der Merwe, eds. New Developments on Fundamental Problems in Quantum Physics (Kluwer, N.Y. 1997

Scientific paper

We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.

Affiliated with

Also associated with

No associations

Rating

Quantum Mechanics on discrete space and time 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 Quantum Mechanics on discrete space and time, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Mechanics on discrete space and time will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-653598