Problem Set

Problem Set 5 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. 2. The normalized ground state wave function for the electron in hydrogen is ψ(r, θ, φ) = π 1/2 a−3/2 e−r/ao o where r is the radial coordinate of the electron and ao 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 = ao /2 and x2 = 3ao /2. 3. A particle with kinetic energy E moves from a region where the potential is zero to one in which the potential is Vo , at x = 0, and E > Vo . (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 Vo . Hint, the particle flux is velocity times probability amplitude and you should normalize the reflecting and transmitting flux by division of the incident flux of particles. 1

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