3.32 Sspd_chapter 1_part 12_quantum mechanical interpretation of

SSPD_Chapter 1_Part 12_ Quantum Mechanical Interpretation of Resistance in a conductor.

1.12. SCATTERING OF CONDUCTING ELECTRONS AND RESISTIVITY OF SOLIDS.

Here we are dealing with a 3-D orderly configuration of atoms arranged as a single crystal of infinite dimensions. We have already seen that electron has all the properties of light wave namely: Bragg reflection, refraction , interference and diffraction. Therefore scattering of electrons cannot be understood in a classical manner.

Liquid state of matter causes fifty times more scattering of electron as compared to the gaseous state of matter where as liquid is thousand times more dense. Therefore extent of scattering does not depend on the density of scattering centers but on the disorderly arrangement of the scattering centers. Here it will be proper to point out as to exactly what the difference is between scattering and reflection.

A smooth plane reflects light whereas a rough plane scatters light. In reflection the angles of incidence are identical hence angles of reflection are identical. As a result the total incident beam of light is reflected. In a rough plane, the constituent rays of the light beam are reflected in different directions since the angles of incidence are different for different rays. This is known as scattered light. These two phenomenon are shown in Figure(1.68).

Figure 1.68. Reflection and Scattering.

Electron is a matter wave probability amplitude matter wave. In 3-D orderly crystalline solid the propagation of electron causes the interaction with and vibration of all the intervening lattice centers. The lattice centers become the emitters of secondary wavelets.

The secondary wavelets interfere and propagate forward in the direction of constructive interference.

1. If the crystal is at 0 Kelvin then there is no thermal vibration. Also assume that there are no crystal defects and that there are no impurities.
2. Also the crystalline lattice in not bounded by surfaces and is infinite in the three directions.
3. Also electrons are in the outer partially filled conduction band well removed from the upper edge of the conduction band.

If all these conditions are fulfilled then the direction of constructive interference will be the direction of incidence and electron will propagate forward as if there is no obstacle in its path. The first impulsive energy will sustain the electron in a straight line propagation path with uniform velocity with no dissipation of energy. This propagation will continue for infinite time and till infinite distance. This is exactly as Newton had predicted about the inertness of bodies: A body at rest will continue to be at rest and a body in motion will continue to be in motion in a straight line with an uniform velocity unless made to act otherwise by the application of force.

This is what is more popularly known as SUPERCONDUCTIVITY.