Basics

Basics

1. Compton Scattering

   • X-rays are scattered by electrons in a material
   • Difference in wavelength = (h/mc)*(1-cos(angle))

2. Electron Diffraction

   • Electrons are diffracted like a wave when passed through a crystal
   • De Broglie relation predicts this behaviour
     • λ = h/p

3. Heisenberg's Uncertainty Principle

   • Position and momentum are complementary variables (incompatible)
   • Δp. Δx ≥ ħ/2

4. Schrodinger Equation

   • Time Dependent
     • From the double slit experiment
       • Ψ(x,t) = Aexp(i(hx-ωt))
       • iħ(∂Ψ/∂t) = -(ħ2/2m)(∂2Ψ/∂x2) + VΨ
   • Time Independent
     • By separating the variables in the TDSE, V(x) is independent of time
       • Solution is a product: Ψ(x,t) = u(x)T(t)
         • T(t) = T0exp(-Et/ħ)
     • -(ħ2/2m)(∂2u(x)/∂x2) + V(x)u(x) = Eu(x)
   • Probability depends on the square of the wavefunction P(x).dx = |u(x)|^2.dx
   • Normalisation
     • Particle must be somewhere: integral over the whole area must equal 1
     • Boundary conditions
       • Continuous, single-valued
       • Finite (see integral)
       • Derivative with respect to position must be continous
         • Unless V(x) is infinite