Useful information, quantum mechanics expectation

Similar to quantum mechanics, which can be formulated in terms of different quantities in addition to the traditional wave function formulation, in quantum chemistry a number of alternative tools are developed for this purpose, which may be useful in the context of the present book. We have already described different approximate models of representing the electronic structure using (many-electronic) wave functions. The coordinate and second quantization representations were employed to get this. However, the entire amount of information contained in the many-electron wave function taken in whatever representation is enormously large. In fact it is mostly excessive for the purpose of describing the properties of any molecular system due to the specific structure of the operators to be averaged to obtain physically relevant information and for the symmetry properties of the wave functions the expectation values have to be calculated over. Thus some reduced descriptions are possible, which will be presented here for reference. 

Turning now to the nanosecond time regime (lower half of Fig. 11), the emitted photons from a single molecule can provide still more useful information. On the time scale of the excited state lifetime, the statistics of photon emission from a single quantum system are expected [84] to show photon antibunching, which means that the photons space themselves out in time , that is, the probability for two photons to arrive at the detector at the same time is small. This is a uniquely quantvun-mechanical effect, which was first observed for Na atoms in a low-density beam [85]. Antibunching is fundamentally measured by computing the second-order correlation of the electric field (r) (whieh is simply the normalized form of the intensity-... 

Figure 7.14 clearly reveals the deviation from the expected, calculated radiative lifetime beyond v = 3. Using these calculated unperturbed values for T, the predissociation rate constants can be extracted from the measured radiative lifetime values (see Table 7.1 for a summary), and these in turn can be used to deduce information about the quantum-mechanical coupling matrix elements. 

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