A new general subset of coherent states, which is complete and overcomplete by just one element, is introduced. It is the union of $N$ arbitrary nonintersecting von Neumann lattices whose unit-cell areas have a harmonic mean of $\mathrm{Nh}$ . First applications are given in the problems of crystal electrons in rational magnetic fields, incommensurate structures in a magnetic field, and quantum dynamics.A new general subset of coherent states, which is complete and overcomplete by just one element, is introduced. It is the union of $N$ arbitrary nonintersecting von Neumann lattices whose unit-cell areas have a harmonic mean of $\mathrm{Nh}$. First applications are given in the problems of crystal electrons in rational magnetic fields, incommensurate structures in a magnetic field, and quantum dynamics.

Physical Review AOct 1, 19833 citations

Generalized coherent states and some of their applications

A. M. Perelomov

Uspekhi Fizicheskih NaukJan 1, 1977119 citations

von Neumann's hypothesis concerning coherent states

J. Žák

An orthonormal basis of modified coherent states is constructed. Each member of the basis is an infinite sum of coherent states on a von Neumann lattice. A single state is assigned to each unit cell of area h (Planck constant) in the phase plane. The uncertainties of the coordinate x and the square of the momentum p 2 for these states are shown to be similar to those for the usual coherent states. Expansions in the newly established set are discussed and it is shown that any function in the kq -representation can be written as a sum of two fixed kq -functions. Approximate commuting operators for x and p 2 are defined on a lattice in phase plane according to von Neumann's prescription.An orthonormal basis of modified coherent states is constructed. Each member of the basis is an infinite sum of coherent states on a von Neumann lattice. A single state is assigned to each unit cell of area h (Planck constant) in the phase plane. The uncertainties of the coordinate x and the square of the momentum p 2 for these states are shown to be similar to those for the usual coherent states. Expansions in the newly established set are discussed and it is shown that any function in the kq -representation can be written as a sum of two fixed kq -functions. Approximate commuting operators for x and p 2 are defined on a lattice in phase plane according to von Neumann's prescription.

Journal of Physics A Mathematical and GeneralOct 8, 200310 citations

A new general subset of coherent states, which is complete and overcomplete by just one element, is introduced. It is the union of

N

arbitrary nonintersecting von Neumann lattices whose unit-cell areas have a harmonic mean of

\mathrm{Nh}

. First applications are given in the problems of crystal electrons in rational magnetic fields, incommensurate structures in a magnetic field, and quantum dynamics.