| Issue |
EPL
Volume 83, Number 1, July 2008
|
|
|---|---|---|
| Article Number | 10007 | |
| Number of page(s) | 4 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/83/10007 | |
| Published online | 18 June 2008 | |
Simultaneous measurement of coordinate and momentum on a von Neumann lattice
Department of Physics, Technion-Israel Institute of Technology - Haifa 32000, Israel
Corresponding authors: ady@physics.technion.ac.il revzen@physics.technion.ac.il zak@physics.technion.ac.il
Received:
15
May
2008
Accepted:
24
May
2008
It is shown that on a finite phase plane the kq-coordinates and the sites of a von Neumann lattice are conjugate to one another. This elementary result holds when the number M defining the size of the phase plane can be expressed as a product, M = M1M2, with M1 and M2 being relatively prime. As a consequence of this result a hitherto unknown wave function is defined giving the probability of simultaneously measuring the momentum and coordinate on the von Neumann lattice.
PACS: 03.65.-w – Quantum mechanics / 04.60.Ds – Canonical quantization / 04.60.Nc – Lattice and discrete methods
© EPLA, 2008
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