Superposition, quantum phenomenon

The quasiclassical trajectory method disregards completely the quantum phenomenon of superposition (13,18,19) consequently, the method fails in treating the reaction features connected with the interference effects such as rainbow or Stueckelberg-type oscillations in the state-to-state differential cross sections (13,17,28). When, however, more averaged characteristics are dealt with (then the interference is quenched), the quasiclassical trajectory method turns out to be a relatively universal and powerful theoretical tool. Total cross-sections (detailed rate constants) of a large variety of microscopic systems can be obtained in a semiquantitative agreement with experiment (6). 

In spite of the apparent obviousness of the beat effect in optical radiation at pulsed excitation, it was only registered and studied comparatively recently. At the beginning of the 1960s Aleksandrov [3] and, independently, Dodd and coworkers [119] discovered beats in atomic emission. It may be pointed out that this, and the related phenomenon of beat resonance, was predicted by Podgoretskii [313], as well as by Dodd and Series [118]. The phenomenon was treated on the basis of well-known fundamental concepts on coherent superposition of states, and was named accordingly quantum beats. These ideas are amply expounded in reviews and monographs [4, 5, 6, 71, 96, 120, 146, 182, 188, 343, 348, 388]. 

This way of imposing classical structures by hand by simply omitting the superpositions between certain chosen states is a very common procedure. Often, the same phenomenon (e.g., the spectrum of ammonia) can be explained in different ways (with, e.g., pyramidal nonstationary states instead of eigenstates), giving a chemical or a quantum-mechanical explanation in our sense. Nevertheless, such differing explanations are not mutually compatible (and may sometimes even be complementary), since either energy or handedness may be a classical observable, but not both together. 

The next field of applications of elementary catastrophe theory are optical and quantum diffraction phenomena. In the description of short wave phenomena, such as propagation of electromagnetic waves, water waves, collisions of atoms and molecules or molecular photodissociation, a number of physical quantities occurring in a theoretical formulation of the phenomenon may be represented, using the principle of superposition, by the integral... 

What has happened Note that before the transformation the states were indistinguishable by a state measurement of the classical basis 0) and (1) and afterwards they are as different as they could possibly be (i.e. orthogonal). We have now encountered the phenomenon of quantum interference. After the transformation (6.8) of state the amplitudes in front of basis state 1) have an opposite sign and cancel each other. These two terms in the superposition are said to have interfered destructively. On the other hand, the two terms with basis state 0) add up (i.e. they interfere constructively). The opposite happens with state J 2) after transformation (6.8). 

As discussed in Sect. 3.7.2, the oscillation between the singlet-triplet transitions in spin-correlated radical pairs gives rise to a phenomenon known as quantum beats, which was first detected experimentally by Klein and Voltz in 1976 [5] and then independently by Brocklehurst [6]. They arise because the singlet and triplet states are a superposition of several stationary states. Strong spin-orbit coupling, hyperfine coupling or a difference in -factors can induce oscillations between the 5 - 7b states, with a frequency given by the expression [7]... 

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