Debroglie

The time evolution of the wavefunetion E is determined by solving the time-dependent Sehrodinger equation (see pp 23-25 of EWK for a rationalization of how the Sehrodinger equation arises from the elassieal equation governing waves, Einstein s E=hv, and deBroglie s postulate that )i=h/p)... 

Approximations have been reviewed in the case of short deBroglie wavelengths for the nuclei to derive coupled quantal-semiclassical computational procedures, by choosing different types of many-electron wavefunctions. Time-dependent Hartree-Fock and time-dependent multiconfiguration Hartree-Fock formulations are possible, and lead to the Eik/TDHF and Eik/TDMCHF approximations, respectively. More generally, these can be considered special cases of an Eik/TDDM approach, in terms of a general density matrix for many-electron systems. 

In Eq. (67) the classical energy of a free particle, a = mu2, has been substituted, with u its velocity and mv its momentum. Equation (67) is of course the well-known relation of deBroglie. 

X(b, g) Angle of deflection b Impact parameter pgb Angular momentum g Initial relative speed pg Relative momentum 9t(a) Phase shift l Angular momentum quantum number h ft l +1) Angular momentum a — pgffi = 2jr/k Wavenumber of the deBroglie wave ah Relative momentum... 

De Moivre, Abraham 13n deBroglie, Louis 97n Debye, Petrus 344n Descartes, Rend 63n Dewar, Sir James 316n Dirac, PAM 264n... 

DeBroglie, in the mid 1920s, proposed the idea that particles could be treated as waves by the relationship, X = h/mv. This equation related the mass (m) and velocity (v) of a particle to its wavelength (X) by using Planck s constant (h). 

In a classical Bohr orbit, the electron makes a complete journey in 0.15 fs. In reactions, the chemical transformation involves the separation of nuclei at velocities much slower than that of the electron. For a velocity 105 cm/s and a distance change of 10 8 cm (1 A), the time scale is 100 fs. This is a key concept in the ability of femtochemistry to expose the elementary motions as they actually occur. The classical picture has been verified by quantum calculations. Furthermore, as the deBroglie wavelength is on the atomic scale, we can speak of the coherent motion of a single-molecule trajectory and not of an ensemble-averaged phenomenon. Unlike kinetics, studies of dynamics require such coherence, a concept we have been involved with for some time. 

Election motion Nuclear motion DeBroglie wavelength... 

Electrons of 150 eV and neutrons of 0.1 eV possess a DeBroglie wavelength of about 1 A, which matches the elementary lattice dimensions in crystals. The appreciable scattering cross sections for electrons causes them to be strongly absorbed and thus... 

Example Problem What is the deBroglie wavelength of a neutron moving with the average Fenni energy in a 208Pb nucleus You can assume that the neutron is nonrelativistic and use r0 = 1.2 fm. 

Classical and Quantum Mechanics. At the beginning of the twentieth century, a revolution was brewing in the world of physics. For hundreds of years, the Newtonian laws of mechanics had satisfactorily provided explanations and supported experimental observations in the physical sciences. However, the experimentalists of the nineteenth century had begun delving into the world of matter at an atomic level. This led to unsatisfactory explanations of the observed patterns of behavior of electricity, light, and matter, and it was these inconsistencies which led Bohr, Compton, deBroglie, Einstein, Planck, and Schrn dinger to seek a new order, another level of theory, ie, quantum theory. 

L. deBroglie, The Revolution in Physics, Noonday Press, Inc., New York, 1953 H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry, John Wiley... 

L. DeBroglie, The Revolution in Physics, Noonday Press, New York, 1953. 

Figure 19. Photon energy dependence of the photoionization cross section intensity of photoelectron peak varies depending upon input photon energy, due to the variation in the deBroglie wavelength of outgoing electron. These wavelengths are compared to the radial wavefunctions of Cu 3d and Cl 3p orbitals. Reproduced from Ref. 28. Copyright 1985, American Chemical Society.

---