Question 1: A ruby laser emits light of wavelength 694.3 nm. If this light is due to transitions from the n=2 state to the n=1 state of an electron in a box (one dimensional), find the width of the box.

Question 2: The normalized ground state wave function for the electron in hydrogen is

ψ(r, θ, φ) = π ^1/2 a_o^-3/2 e ^-r/ao

Where r is the radial coordinate of the electron and a_o is the Bohr radius.

(a) Sketch the wave function as ψ(r) verses r.

(b) Show that the probability of finding the electron between r and r + dr is given by 4πr²|ψ(r)|dr.

(c) Show that the wave function is normalized.

(d) Find the probability of locating the electron between x₁ = a_o/2 and x₂ = 3a_o/2.

Question 3: A particle with kinetic energy E moves from a region where the potential is zero to one in which the potential is V_o, at x = 0, and E > V_o.

(a) What happens classically?

(b) What happens quantum mechanically? Derive the probabilities for reflection and transmission through the potential, leave your answer in terms of E and V_o.