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Coherent state

Coherent states and diverse semiclassical approximations to molecular wavepackets are essentially dependent on the relative phases between the wave components. Due to the need to keep this chapter to a reasonable size, we can mention here only a sample of original works (e.g., [202-205]) and some summaries [206-208]. In these, the reader will come across the Maslov index [209], which we pause to mention here, since it links up in a natural way to the modulus-phase relations described in Section III and with the phase-fiacing method in Section IV. The Maslov index relates to the phase acquired when the semiclassical wave function haverses a zero (or a singularity, if there be one) and it (and, particularly, its sign) is the consequence of the analytic behavior of the wave function in the complex time plane. [Pg.108]

The time dependence of the molecular wave function is carried by the wave function parameters, which assume the role of dynamical variables [19,20]. Therefore the choice of parameterization of the wave functions for electronic and nuclear degrees of freedom becomes important. Parameter sets that exhibit continuity and nonredundancy are sought and in this connection the theory of generalized coherent states has proven useful [21]. Typical parameters include molecular orbital coefficients, expansion coefficients of a multiconfigurational wave function, and average nuclear positions and momenta. We write... [Pg.224]

The generalized Prony analysis can extract a great variety of information from the ENDyne dynamics, such as the vibrational energy vib arrd the frequency for each normal mode. The classical quantum connection is then made via coherent states, such that, say, each nomral vibrational mode is represented by an evolving state... [Pg.240]

Also, rotational state resolution of cross-sections can be obtained by employing a coherent state analysis [51] for the situation of weak coupling between rotational and vibrational degrees of freedom. A suitable rotational coherent state can be expressed as... [Pg.244]

From these relations it follows that is related to the angular momentum modulus, and that the pairs of angle a, P and y, 8 are the azimuthal, and the polar angle of the (J ) and the (L ) vector, respectively. The angle is associated with the relative orientation of the body-fixed and space-fixed coordinate frames. The probability to find the particular rotational state IMK) in the coherent state is... [Pg.244]

The use of the rotational coherent state is then analogous to the use of the vibrational coherent state and can be used to study rotational state resolved properties. We note that the resolution of the identity applies here as well, that is. [Pg.244]

Electron Nuclear Dynamics (48) departs from a variational form where the state vector is both explicitly and implicitly time-dependent. A coherent state formulation for electron and nuclear motion is given and the relevant parameters are determined as functions of time from the Euler equations that define the stationary point of the functional. Yngve and his group have currently implemented the method for a determinantal electronic wave function and products of wave packets for the nuclei in the limit of zero width, a "classical" limit. Results are coming forth protons on methane (49), diatoms in laser fields (50), protons on water (51), and charge transfer (52) between oxygen and protons. [Pg.13]

Classical dynamics is studied as a special case by analyzing the Ehrenfest theorem, coherent states (16) and systems with quasi classical dynamics like the rigid rotor for molecules (17) and the oscillator (18) for various particle systems and for EM field in a laser. [Pg.29]

Klauder, J. R. Skagerstam, B.-S. Coherent States, Applications in Physics and Mathematical Physics World Scientific Singapore, 1985. [Pg.32]

Perelomov A. M., "Generalized Coherent States and their Applications" Springer, New York, 1986. [Pg.242]

It is known that if the system described by the Hamiltonian in Eq. (146) has been in a coherent state a(0) = a and /3m(0) = pm at the initial moment of time, then its state will also be a coherent one at subsequent moments of time, and the dependence of the eigenvalues on time will be determined by the coupled equations... [Pg.164]

R J Glauber, in Coherent States in Quantum Theory, Mir, Moscow, 1972, p 26... [Pg.175]

The ground-state effective Hamiltonian is diagonal with eigenvalues ha n + 5], whereas the excited state one is that of a driven quantum harmonic oscillator that must lead to coherent states. [Pg.254]

Semiclassics and propagation of coherent states for spin-orbit coupling problems... [Pg.97]

Abstract. The Dirac equation is discussed in a semiclassical context, with an emphasis on the separation of particles and anti-particles. Classical spin-orbit dynamics are obtained as the leading contribution to a semiclassical approximation of the quantum dynamics. In a second part the propagation of coherent states in general spin-orbit coupling problems is studied in two different semiclassical scenarios. [Pg.97]

Keywords Dirac equation, semiclassics, spin-orbit coupling, coherent states... [Pg.97]


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Annihilation operator coherent states

Atomic ions trapped, coherent quantum state

Canonical coherent states

Classical coherent states

Coherence/coherent states

Coherence/coherent states

Coherent Spin-State Mixing

Coherent dark states

Coherent excitation of an autoionising state

Coherent excitation of continuum states

Coherent state density matrix

Coherent state group-theoretic states

Coherent state prefactor

Coherent state properties

Coherent state transition amplitude

Coherent state wavefunction

Coherent states , second-harmonic

Coherent states Floquet Hamiltonian

Coherent states Fock representation

Coherent states STIRAP)

Coherent states atomic transitions

Coherent states bond vibrations

Coherent states conductivity

Coherent states coupling

Coherent states expectation values

Coherent states experimental results

Coherent states general properties

Coherent states generalized phase

Coherent states hydrogen bonds

Coherent states mechanisms

Coherent states molecular associates

Coherent states molecular clustering

Coherent states molecular photonics, quantum

Coherent states molecular systems

Coherent states nonlinear oscillator generation

Coherent states operators

Coherent states photon exchange

Coherent states pulsed nuclear magnetic resonance

Coherent states pump photonics

Coherent states quantum interference

Coherent states quantum mechanics

Coherent states quantum optics

Coherent states radiation phase structure

Coherent states statistical mechanical approach

Coherent states stimulated Raman adiabatic passage

Coherent states structural physical effects

Coherent states subsystem dynamics

Coherent states superposition

Coherent states switching

Coherent states thermodynamics

Coherent states tunneling

Coherent superposition of states

Coherent superposition state motion

Coherent-state theory

Equilibrium density operator, coherent states

Finite-dimensional coherent states

Finite-dimensional phase-coherent states

Gaussian coherent state

Glauber coherent states

Group coherent state

Hilbert space coherent states

Intermediate state, in coherence transfer

Laser pulses, quantum dynamics coherent states

Odd and even coherent states

Projective coherent states

Quantum harmonic oscillator coherent states

Quantum states coherence

Resonances coherent state superposition

Spin-coherent state

Surface excitons coherent states

Time-dependent molecular theory coherent states

Two-dimensional coherent states

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