Time-independent quantum-mechanical

A time-independent quantum mechanical study by Engel and coworkers (1985) gave qualitatively the same results as the time dependent analog and the quassi classical trajectory method. A quantum theory for probing transition-state absorption/emission has also been developed by Lee et al. (1989). 

Let us make this more quantitative using the time-independent quantum mechanical theory outlined in Section 3.1. Because the interaction potential is independent of r the potential matrix V defined in (9.2) is diagonal, i.e., different vibrational fragment states do not mutually couple. As a result, the matrix of radial wavefunctions Xri (A, r E, n), which solve the coupled equations (3.5), is diagonal as well, i.e., Xri E,n) o< firm - If we assume, in order to simplify the subsequent discussion, that the nuclear wavefunction in the ground electronic state factorizes as pr R) final state n and the unnormalized final state distribution becomes... 

Molecular time-independent Quantum Mechanics (QM), including Density Functional Theory (DFT),... 

Time-Independent Quantum-Mechanical Spectral Analysis 154... 

TIME-INDEPENDENT QUANTUM-MECHANICAL SPECTRAL ANALYSIS... 

The first exact quantum calculations of integral and differential cross sections on the adiabatic state were reported in 2001 by Honvault and Laimay [15,81]. They have carried out quantum reactive scattering calculations of the title reaction on the DK PES within the Time Independent Quantum Mechanical (HQM) framework using the hyperspherical close-coupling method. 

NON-ADIABATIC DYNAMICS IN THE O-I-H2 REACTION A TIME-INDEPENDENT QUANTUM MECHANICAL STUDY... 

The remaining (n - 1 )A photons are removed at time r and the decay of the excited states is monitored. After t the system again is described by the time independent quantum mechanical Hamiltonian H, so the state is... 

Time-independent quantum mechanics gives transition frequencies and intensities for static systems (solids) or systems in the fast motion limit (solutions) subject to J-coupHng, chemical shift, and quadrupolar coupling interactions. 

The solution-state H NMR spectrum of 1-chloroethene (Fig. 7.1) is easily described by time-independent quantum mechanics using an uncoupled basis set of spin functions. The total Hamiltonian is... 

It is quite easy to see that the new orbitals in Equation 2.66 are directed. For example, Xi has a larger value in the point (x, y, z) = (1,1,1) than in the point (-1, -1, -1). The other orbitals are directed in the (-1, -1,1), (-1,1, -1), and (1, -1, -1) directions, that is, toward the comers of a regular tetrahedron (or every second comer of a cube). This is the quantum mechanical description of the Lewis electron pairs. In time-independent quantum mechanics, we are interested in probability distributions. The electrons require a region of a certain size, sp -hybridization shows that if the 2s and 2p AOs are accessible, four bonds can be found with as little overlapping as possible. The new orbitals no longer have the nucleus as an inversion center. 

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