Showing papers on "Coherent states in mathematical physics published in 1980"
TL;DR: In this paper, it is shown on examples that the distance between nearby states is related to quantum fluctuations; in particular, in the particular case of the harmonic oscillator group the condition of zero curvature appears to be identical to that of non dispersion of wave packets.
Abstract: A metric tensor is defined from the underlying Hilbert space structure for any submanifold of quantum states. The case where the manifold is generated by the action of a Lie group on a fixed state vector (generalized coherent states manifold hereafter noted G.C.S.M.) is studied in details; the geometrical properties of some wellknown G.C.S.M. are reviewed and an explicit expression for the scalar Riemannian curvature is given in the general case. The physical meaning of such Riemannian structures (which have been recently introduced to describe collective manifolds in nuclear physics) is discussed. It is shown on examples that the distance between nearby states is related to quantum fluctuations; in the particular case of the harmonic oscillator group the condition of zero curvature appears to be identical to that of non dispersion of wave packets.
520 citations
TL;DR: In this article, a generalized Heisenberg-type uncertainty relation is obtained for two arbitrary operators both in the case of pure and of mixed states, and as a rule equality is found to hold for pure quantum state only.
265 citations
01 Jan 1980
TL;DR: The coherent states of the harmonic oscillator and hence the radiation field (which is considered as an assembly of oscillators) can be defined in many different, but essentially equivalent ways as mentioned in this paper.
Abstract: The coherent states of the harmonic oscillator and hence the radiation field (which is considered as an assembly of oscillators) can be defined in many different, but essentially equivalent ways.1
47 citations
TL;DR: In this paper, a path integral representation for the transition amplitude which joins arbitrary initial and final states is derived, and the time-dependent Hartree-Fock is naturally obtained as a classical limit.
46 citations
TL;DR: In this article, it was shown that the expectation value of the quantum Hamiltonian in any coherent state equals the energy of the classical field at which the state is peaked, and that this property can be used to characterize the usual Fock representation.
Abstract: In the usual Fock quantisation of fields in Minkowski space-time, one has the result that the expectation value of the quantum Hamiltonian in any coherent state equals the energy of the classical field at which the state is peaked. It is shown that this property can be used tocharacterise the usual Fock representation. It is also pointed out that the entire analysis goes through for a substantially more general class of systems including, in particular, Bose fields in arbitrary stationary space-times.
30 citations
01 Jan 1980
TL;DR: In this paper, the authors presented an approximate Schrodinger evolution for Gaussian states with the Trotter Product Formula and the second order Taylor expansion of the potential about the center of the wave packet.
Abstract: For certain Gaussian states we present a simple approximate evolution which is asymptotic to the Schrodinger evolution as
→ O.In 3 or more dimensions our error estimates are uniform in time if the potential is suitably chosen. Consequently, our methods apply to scattering theory. The approximate evolution is obtained by using the Trotter Product Formula and the second order Taylor expansion of the potential about the center of the wave packet.
18 citations
11 citations
TL;DR: In this paper, a quantum-classical correspondence for the oscillator cranking model is established through a set of coherent states of the Heisenberg symplectic group N(2)(X)Sp(4,R).
Abstract: The oscillator cranking-model wavefunction can be identified with a set of coherent states of the symplectic group Sp(4,R). A quantum-classical correspondence for the model is, however, established through a set of coherent states of the Heisenberg symplectic group N(2)(X)Sp(4,R). The properties of these states and their usefulness in various fields of physics are studied in detail. Interesting and useful generalisations of these coherent states are also discussed.
6 citations