Bohme

Bohme D K and Raksit A B 1984 Gas phase measurements of the influence of stepwise soivation on the kinetics of nucieophiiic dispiacement reactions with CHjCi and CHjBr at room temperature J. Am. Ghem. Soc. 106 3447-52... 

B. Vector-Potential Theory The Molecular Aharonov-Bohm Effect... 

The simplest choice v /(Q) = where p is a half-odd integer and 4> is an angle measured around the degeneracy, is therefore nonnally employed in molecular Aharonov-Bohm theory. 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

The aim of this section is to show how the modulus-phase formulation, which is the keytone of our chapter, leads very directly to the equation of continuity and to the Hamilton-Jacobi equation. These equations have formed the basic building blocks in Bohm s formulation of non-relativistic quantum mechanics [318]. We begin with the nonrelativistic case, for which the simplicity of the derivation has... 

F. D. Peat, Infinite Potential, The Life and Times of David Bohm, Addison-Wesley, Reading, MA, 1997, p. 192. 

M. Peshkin and A, Tonomura, The Aharonov Bohm Effect, Springer-Verlag, Berlin, 1989. 

D. Bohm, Quantum Theory, Prentice-Hall, New York, 1952. 

The phase-change nale, also known as the Ben phase [101], the geometric phase effect [102,103] or the molecular Aharonov-Bohm effect [104-106], was used by several authors to verify that two near-by surfaces actually cross, and are not repelled apart. This point is of particular relevance for states of the same symmetry. The total electronic wave function and the total nuclear wave function of both the upper and the lower states change their phases upon being bansported in a closed loop around a point of conical intersection. Any one of them may be used in the search for degeneracies. 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

The quantum mechanical importance of a vector potential A, in regions where the magnetic field is zero, was first recognized by Aharonov and Bohm in their seminal 1959 paper [112]. 

H.-J. Bohm, G. Klebe, H. Kubinyi, Wirkstoffdesign, Spektrum Akademisdier Verlag, Heidelberg, 1996. 

H.-J. Bohm, G. Schneider (Eds.), Virtual screening for bioactive molecules, in Methods and Principles in Medicinal Chemistry, Vol. 10, R. Marmhold, H. Kubinyi, H. Timmerman (Eds.), Wiley-VCH, Weinheim, 2000, pp. 1-307... 

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