Showing papers on "Coherent states in mathematical physics published in 1979"

Coherent states and the resonance of a quantum damped oscillator

Abstract: A quantum-mechanical model of a damped harmonic oscillator (both with time-independent and time-dependent parameters) is studied in the framework of the linear Schr\"odinger equation with a Hermitian nonstationary Hamiltonian. Integrals of the motion of this equation and their eigenstates, including coherent states, are constructed. The influence of an external harmonic force to the time evolution of various average values calculated over coherent states is considered, including the resonance case. The specific symmetry of the Hamiltonian leading to the new concept of loss-energy states is discussed.

Coherent states for general potentials. I. Formalism

Abstract: We first review the properties of the harmonic-oscillator coherent states which can be equivalently defined as (a) a specific subset of the x-p minimum-uncertainty states, (b) eigenstates of the annihilation operator, or (c) states created by a certain unitary exponential displacement operator. These definitions are not equivalent in general. Then we present a new method for finding coherent states for particles in general potentials. Its basis is the desire to find those states which most nearly follow the classical motion, but it is most nearly a generalization of the minimum-uncertainty method. The properties of these states are discussed in detail. Next we show that the annihilation operator and displacement operator methods, as heretofore defined, cannot be applied to general potentials (whose eigenvalues are not equally spaced). We define a generalization of these methods but show that the states so defined are not, in general, equivalent to the minimum-uncertainty coherent states. We discuss a number of properties of our coherent states and the procedures we have used.

Coherent states for general potentials. II. Confining one-dimensional examples

Abstract: We apply our minimum-uncertainty coherent-states formalism, which is physically motivated by the classical motion, to two confining one-dimensional systems: the harmonic oscillator with centripetal barrier and the symmetric P\"oschl-Teller potentials. The minimum-uncertainty coherent states are discussed in great detail, and the connections to annihilation-operator coherent states and displacement-operator coherent states are given. The first system discussed provides an excellent bridge between the harmonic oscillator and more general potentials because, even though it is a nonharmonic potential, its energy eigenvalues are equally spaced. Thus, its coherent states have many, but not all, of the properties of the harmonic-oscillator coherent states.

Generalized Coherent States and the U (n) Lie Group

Abstract: In this paper we study the generalized coherent states (gcs) in n -dimensional space Their annihilation operators consist of linear combinations of the annihilation operators a l , and their coherent states are the product of the simple coherent states All the known annihilation operators which have been studied as yet, and also the magnetic ones, are special cases of these operators The new operators A k + A m form the Lie algebra U ( n ) of the Lie group U ( n ) Finally, instead of the operators a l and a l + we can use the new operators, which depend on a complex parameter