DeBroglie equation

Neutron scattering involves interactions of a neutron beam with atomic nuclei (Figure 4.3). The wave like nature of a beam of neutron particles each with mass M is incorporated in the deBroglie equation which states that the wave length of a neutron beam, A, is inversely proportional to the particle velocity, v, or... 

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)... 

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. 

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). 

The union of deBroglie s, Planck, Heisenberg, Schrodinger and Bohr s ideas lead to the development of the wave-mechanical view of the atom. The solution to Schrodinger s equation provides for 3 quantum numbers added to Pauli s idea that no two electrons could have the same solution set for Schrodinger s equation (known as Pauli exclusion principle), we have four quantum numbers that describe the most probable orbital for an electron of a given energy or the quantum mechanical model of the atom. 

The constant k is also related to the wavelength through the deBroglie relationship, as shown in Equation (I 1.14). 

E. Schrodinger (1926), following the earher work of L. deBroglie (1924), advanced a fundamental equation of wave mechanics. The Schrodinger equation of wave mechanics was developed for waves oscillating in three dimensions with co-ordinates x, y and z ... 

Figure 2 Electron mobility and deBroglie wavelength (Equation 4).

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