Eigenstate zero-point

Stimulated emission pumping spectra of HCP X1 have been recorded via the A lA" [12] and C lA states [5]. These 0.05-cm-1 resolution spectra sample eigenstates rather than feature states, extending to Vib - 25,315 cm-1, above the X state zero-point level, about 1300 cm-1 above the ab initio predicted linear HPC saddle point [5, 13]. 

Now, perform the trace over the eigenstates of the slow mode quantum harmonic oscillator involved in the ACF (114). This leads, after neglecting the zero-point energy of H-bond bridge oscillator, to... 

Again, introduce the closeness relation (76) on the eigenstates of the slow mode harmonic oscillator and neglect the zero-point energy of the Boltzmann operator. This gives... 

Although Einstein s theory accounts well for the relative amplitudes of absorption, fluorescence and stimulated emission, the notion that fluorescence occurs spontaneously is fundamentally inconsistent with the assertion we made in Chap. 2 that an isolated system is stable indefinitely in any one of its eigenstates. If the latter principle is correct, fluorescence must be caused by some perturbation we have neglected. The quantum theory of radiation provides a way out of this conundrum. As we discussed in Chap. 3, a radiation field has an eigenstate in which the number of photons is zero. Spontaneous fluorescence can be ascribed to perturbation of the excited molecule by the zero-point radiation field [26,27]. Let s examine this rather xmsettling idea. 

In light alkali atoms, Li and Na, the fine structure splitting of a low state is typically much larger than the radiative decay rate but smaller than the interval between adjacent states. In zero field the eigenstates are the spin orbit coupled tsjnij states in which and s are coupled. However, in very small fields and s are decoupled, and the spin may be ignored. From this point on all our previous analysis of spinless atoms applies. How the passage from the coupled to the uncoupled states occurs depends on how rapidly the field is applied. It is typically a simple variant of the question of how the m states evolve into Stark states. When... 

As already pointed out, a room-temperature sample provides a rich source of molecules in high rotational states. However, in order to rotationally select a molecule in a photodissociation reaction, it is necessary to have assignable lower and upper states. Aside from the considerable problem associated with extreme anharmonicity near the dissociation limit, many molecules are in the ergodic limit and have intrinsically unassignable eigenstates. That is, the eigenstates consist of random admixtures of zero-order basis states as in the case of H2CO (Polik et al., 1990). 

The radial function is shown in Figure 8-1, and the radial distribution function (r R) for this eigenstate is shown in Figure 8-2. The radial function has one node at r = 2ao representing a point of zero probability. 

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