Coherent states molecular associates

A more realistic model for the secondary relaxation needs to consider motions of a molecular group (considered as a rigid object) between two levels. The group may contain N atoms with the scattering length h, at positions r (i=lj ). The associated motion may consist of a rotation aroimd an arbitrary axis, e.g. through the centre of mass depicted by a rotational matrix Q and a displacement by a translational vector . In order to evaluate the coherent dynamic structure factor, scattering amphtudes of the initial (1) and final (2) states have to be calculated ... 

Once this discussion of the space-inversion operator in the context of optically active isomers is accepted, it follows that a molecular interpretation of the optical activity equation will not be a trivial matter. This is because a molecule is conventionally defined as a dynamical system composed of a particular, finite number of electrons and nuclei it can therefore be associated with a Hamiltonian operator containing a finite number (3 M) of degrees of freedom (variables) (Sect. 2), and for such operators one has a theorem that says the Hamiltonian acts on a single, coherent Hilbert space > = 3 (9t3X)51). In more physical terms this means that all the possible excitations of the molecule can be described in . In principle therefore any superposition of states in the molecular Hilbert space is physically realizable in particular it would be legitimate to write the eigenfunctions of the usual molecular Hamiltonian, Eq. (2.14)1 3 in the form of Eq. (4.14) with suitable coefficients (C , = 0. Moreover any unitary transformation of the eigen-... 

To derive these and other conclusions, we need to specify the molecular states 7>. Since we are interested in vibrational spectra associated with coherent electronic absorption-emission processes, we represent the molecular states by products of electronic and vibrational wavefunctions... 

If a second pump pulse identical to the first one is illuminating the system after a short delay, its efficiency should be markedly reduced, because all the pairs of atoms at distances R within the PA window [/ min. f max] have been transformed into excited molecules. This void in the pair wavefunction of the initial state, hereafter identified as the dynamical hole, is well known from previous work on coherent confrol [43,53] as one of the main outcomes of excitation of a molecular system with a short laser pulse. It is associated to a momentum kick. The effect is also present in the ulfracold regime [27] and has been analyzed in detail in Ref. [38]. 

An atomic or molecular beam of Ga, As, Al, and/or other elements is created thermally in a ultrahigh-vacuum chamber and directed at a specific, well-defined, atomically flat facet of a single-crystal substrate. A very low deposition rate, associated with a precisely controlled substrate temperature and various real-time techniques for monitoring the state of the surface, permit one to find growth conditions that preserve a coherent crystalline order or minimize the density of structural... 

In its broadest sense, spectroscopy is concerned with interactions between light and matter. Since light consists of electromagnetic waves, this chapter begins with classical and quantum mechanical treatments of molecules subjected to static (time-independent) electric fields. Our discussion identifies the molecular properties that control interactions with electric fields the electric multipole moments and the electric polarizability. Time-dependent electromagnetic waves are then described classically using vector and scalar potentials for the associated electric and magnetic fields E and B, and the classical Hamiltonian is obtained for a molecule in the presence of these potentials. Quantum mechanical time-dependent perturbation theory is finally used to extract probabilities of transitions between molecular states. This powerful formalism not only covers the full array of multipole interactions that can cause spectroscopic transitions, but also reveals the hierarchies of multiphoton transitions that can occur. This chapter thus establishes a framework for multiphoton spectroscopies (e.g., Raman spectroscopy and coherent anti-Stokes Raman spectroscopy, which are discussed in Chapters 10 and 11) as well as for the one-photon spectroscopies that are described in most of this book. 

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