Q1 V(x) a: The figure to the right shows a potential well where V(X)=0 for 0

6. In Dirac notation, after the equation Bø) = b|p)is solved, we often write the solutions as {|Øn)} and {bn}. The name given to {b,} is it is the spectrum of the operator B . Essentially problem 5 and problem 6 are describing identical situations. What is the relationship between pn (x) and |Øn)? To answer this, give a mathematical answer and a physical interpretation of what it means. Hint: If you do not know how to answer this off the top of your head as being obvious, review my notes on Dirac notation and how vectors are used in quantum mechanics.

Q1. Consider the finite square well potential shown in the following diagram: U(x) E>0 L The potential is given by: for xL| -U. for 0 0is incident on this region from the left. Using the plane A particle with energy wave approximation for the particle: a) Show that Y = Ae*+Be¬k* is a suitable general solution to the time-independent Schrödinger wave-equation (TISE) that applies in the region x L write down the four equations arising from the boundary conditions that apply at x=0 and x=L .

Q4. Show that the Legendre polynomials are orthogonal solutions of the angular part of the Schrodinger equation.