Rotational quantum state

Dixon et al. [75] use a simple quantum mechanical model to predict the rotational quantum state distribution of OH. As discussed by Clary [78], the component of the molecular wave function that describes dissociation to a particular OH rotational state N is approximated as... 

Microwaves Excitation between rotational quantum states Rotational spectroscopy... 

We tend to give the letter J to the rotational quantum states. The rotational ground state has a rotational quantum number of J and the excited rotational quantum number is J. To be allowed (in the quantum-mechanical sense), the excitation from J to J must follow... 

The Raman effect is produced when the frequency of visible light is changed in the scattering process by the absorption or emission of energy produced by changes in molecular vibration and vibration-rotation quantum states. 

The UV spectrum of nitrite at acidic pH is unusual. Nitrite at neutral to alkaline pH has a single peak at 356 nm, which is converted to a series of multiple peaks at acidic pH (Fig. 15). Normally, a UV peak is broadened by a combination of vibrational and more closely spaced rotational quantum states. However, light in the near UV region can separate nitrous acid into hydroxyl radical and nitric oxide. 

Interestingly, Miyazaki et al. [1991b) showed that the rate constant depends on the initial rotational quantum state of H2 i.e., reaction (6.50) is three times faster in para-H2 than in ortho-H2. Although the exchange reactions considered here constitute a fundamental reaction system that has been studied by quantum theory for more than half a century, further investigation is needed to understand chemical dynamics in real crystals. 

The OH radical is produced in a particular vibrational and rotational quantum state specified by the quantum numbers n and j. The corresponding energies are denoted by tnj. The probabilities with which the individual quantum states are populated are determined by the forces between the translational mode (the dissociation coordinate) and the internal degrees of freedom of the product molecule along the reaction path. Final vibrational and rotational state distributions essentially reflect the dynamics in the fragment channel. They are one major source of information about the dissociation process. 

Andresen, P., Beushausen, V., Hausler, D., Liilf, H.W., and Rothe, E. (1985). Strong propensity rules in the photodissociation of a single rotational quantum state of vibra-tionally excited H2O, J. Chem. Phys. 83, 1429-1430. 

For reactants in complete thermal equilibrium, the probability of finding a BC molecule in a specific quantum state, n, is given by the Boltzmann distribution (see Appendix A.l). Thus, in the special case of non-interacting molecules the probability PBC(n)y °f finding a BC molecule in the internal (electronic, vibrational, and rotational) quantum states with energy En is... 

Fig. 4.1.13(a-c) shows partial cross-sections for reactions with the reactant molecules in vibrational quantum states n = 0,1,2 and rotational quantum state J = 0 and products in vibrational states n = 0,1,2, respectively, and any rotational quantum state. Note that the abscissa axis in this plot is the translational energy and not the total energy as in Fig. 4.1.12. The translational energy is found in the latter plot by subtracting the molecular energy En

Fig. 4.1.14 shows another example of the calculation of partial cross-sections for product molecules in specified rotational quantum states J and any vibrational quantum state. 

The Gaussian width b of the angular distributions of NO detected in different rotational quantum states (J = 6.5 and 15.5) exhibits comparable values and the same dependence on the desorption velocity,... 

The large Einstein radiative coefficients [225] and the widely spaced vibration-rotation quantum states make HF peculiarly prone to stimulated emission, and a large proportion of the chemical lasers which have been reported operate on lines in the infrared bands of this molecule [224], H-atom abstraction reactions by F and F-atom abstraction by H are both normally exothermic, and HF is quite generally produced in a vibrational distribution giving rise to oscillation. However, the systems are complex frequently both types of reaction occur, and the details of the vibrational distribution resulting from chemical reaction are difficult to evaluate. 

The Stark effect and the Zeeman effect of molecules in an inhomogeneous external field serve to select molecules due to their different rotational quantum states and are thus used to produce molecules with well defined preferential orientations in a beam molecules with different orientation are differently deflected in these fields. With regard to state selectors one can distinguish between simple deflection devices like Stern-Gerlach magnets (and their electrical analogues) and multipole fields where molecules with a well-defined Stark or Zeeman-effect are focused into the detector. In both cases the state selector works as a filter enhancing the relative number of molecules in a certain quantum state. 

There is no mathematical theorem to prove either the existence of electronic wave function such as 4 k(x) independent from instantaneous nuclear coordinates or those of the BO type where there is a parametric dependence on p. What is physically known is the existence of vibrational-rotational quantum states for a given electronic state. It is in this sense that, state functions of the type given by Eq. (7) can be seen as describing such circumstance. 

Magnesium. Excited Mg atoms (3s 3p P ) and PH3 give MgH (v = 0,1) Its nascent rotational quantum state distribution was determined [75]. 

Same as hydrogen, under normal circumstances, deuterium (normal-D2) consists of ortho-D2 and para-D2. However, because the D atom nuclear spin quantum number / = 1 is boson, nuclear exchange symmetry of the total wave function is symmetrical. Para-D2 corresponds to the energy levels at even-number rotational quantum states (7 = 0, 2,4,...) ortho-D2 corresponds to odd-number states 0 =1 3, 5,...). The ratio of ortho-D2 to para-D2 is 2 1. We prepared ortho-D2 using the same method as para-H2. 

We note here that other scenarios for the generation of entanglement between rotational quantum states of two polar molecules have been proposed in Ref. [13]. In that approach, the entanglement arises from dipole-dipole interaction and is controlled by a sequence of laser pulses simultaneously exciting both molecules. In addition to cold molecules trapped in optical lattices, cold molecules in solid matrices are also considered in Ref. [13]. 

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