Chapter05Wave Properties of Matter

General Bibliography

1) Various wikipedia, as specified2) Thornton-Rex, Modern Physics for Scientists &

Eng, as indicated

Chapter 05

• 5.1 X-Ray Scattering• 5.2 de Broglie Waves• 5.3 Electron Scattering• 5.4 Review of Wave Motion• 5.6 Uncertainty Principle• 5.7 Postulates of Quantum Mechanics

Wave-Particle Duality

• Particle-Like Behaviors– Rutherford Scattering– Bohr Model– Photoelectric Effect– Compton Scattering– Pair Production– Positron Annihilation

• Wave-Like Behaviors– X-Ray Diffraction– Bragg Scattering– Electron Scattering– etc

Von Laue Diffraction Patterns

Bragg Scattering

nl = 2 d sinq

Powder X-Ray Diffraction

Davisson & Germer Electron Scattering

Electron Scattering

de Broglie

Basic Wave Review

Superposition of Waves / Fourier Series

Uncertainty Principle for A Simple Case

Mythical “Gaussian” Shaped Wave

-- a specially constructed wave packet that has the smallest possible values for both the product DpDx and DEDt

Postulates of Quantum Mechanics

• All information that can be known about a particle/system is contained within the wavefunction Y(x,t)

• The probability of finding the particle at (x,t) is given by Y* Y.– in a region Dx about (x,t) by Y* Y Dx

• The probability of finding the particle anywhere is 100% or 1.

spaceall

dx*1

Postulates of Quantum Mechanics• Every observable quantity is associated with an “Operator” which is used

to extract the information from the wavefunction

• The expectation value (aka average) of an observable quantity is given by

• The time evolution of the wavefunction is determined by

spaceall

dxOpOporOp *____

rrxx operatoroperator

dt

diH

dx

dip

dt

diE operatorxoperator ,

H = Hamiltonian