Coherent states on von Neumann lattice and some of their applications

Abstract

Coherent states on von Neumann lattice, which form complete but not overcomplete set, are orthogonalized using Löwdin procedure and corresponding coefficients arising in orthogonalization are tabulated. So obtained states may be interpreted as eigenstates of operators of optimal unsharp measurement of coordinate and momentum, in a slightly modified von Neumann sense. Using the obtained results the most important statistical characteristics of these operators are calculated on coherent states and compared with corresponding values of standard quantum mechanical operators of coordinate and momentum.