Quantum and Wave Physics

Question 1

What is the Bragg condition?

Answer 1

nλ = 2dsin(α)

Question 2

What is the equation for phase velocity?

Answer 2

vp = λν = ω/k

Question 3

What is the equation for group velocity?

Answer 3

vg = Δω/Δk

Question 4

Classical and Heisenberg uncertainty principle?

Answer 4

σxσk ≈ 1 and ΔxΔp ≥ h/4π

Question 5

Plane wave solution (complex form)?

Answer 5

Ψ(x,t) = Ae^i(kx−ωt) = [Ψ(x)]e^−iωt

Question 6

What is the Born rule, or normalization condition?

Answer 6

P = ∫ |Ψ(x)|^2 dx, or the integral evaluated to infinity = 1.

Question 7

What was Planck’s law for blackbody radiation, derived by Einstein?

Answer 7

du(f)/df = (8πhf^3/c^3) (1/exp(hf/kT) - 1)

Question 8

What is the definition of a blackbody?

Answer 8

An object in thermodynamic equilibrium, which completely absorbs all incident radiation.

Question 9

What is the equation for Compton scattering?

Answer 9

Δλ = (h/mc) (1-cosθ)

Question 10

What two pieces of evidence did de Broglie use to theorize the idea of matter waves?

Answer 10

a) showing that the group velocity of the wave packet v_g = pc^2/E
b) experimental evidence of diffraction patterns obtained when electrons scattered off gold film

Question 11

What is the single-slit diffraction approximation to Heisenberg’s uncertainty principle?

Answer 11

ΔyΔp_y .=. h

Question 12

How is a ‘free’ particle defined?

Answer 12

A particle in a spatial region where the potential, V is either 0 or constant.

Question 13

For a free particle, how is the angular frequency ω related to the wave number k?

Answer 13

ω(k) = hk^2/4πm

Question 14

Scrodinger originally theorized that the electric charge density of a moving wave packet is given by ρe = e(Ψ^2). Why is this wrong?

Answer 14

Because the wave packet disperses as it moves through spacetime.

Question 15

How can wavelength in the single slit experiment be approximated?

Answer 15

λ = aL/2D