1. ConcepTest #65 Consider the following graph of a wave function for a particle. a) At what point(s) are you most likely to find the particle? Hold up as many cards as needed. b) At what point(s) are you least likely to find the particle? Hold up as many cards as needed.

2. ConcepTest #66 Consider the following graph of probability density P(x) versus x (where P(x) = |  (x)| 2 ) for some particle. You want to determine the probability of finding the particle in a region around some point x 0. Which of the following will allow you to calculate this? 1. Height of the curve 2. Area under the curve 3. Slope of the curve 4. Concavity of the curve 5. Number of zeroes 6. None of the above

3. ConcepTest #67 Consider the following graphs of the wave function  (x) for a particle of mass m confined to a one dimensional box of length L. Each graph represents a different state the particle can be in. In which state does the particle have the larger (magnitude) of momentum?

4. ConcepTest #68 A particle confined to a one dimensional region of length L is in its 2 nd excited state (third mode), as shown in the diagram. The normalized wave function for the particle is. What is the probability of finding the particle in the region between x = 0 and x = L /3?

5. Example: Calculating Probability from Wave Function A particle of mass m confined to a box of length L is in its ground (lowest energy) state. The normalized wave function for the particle is. Determine the probability of finding the particle in the region between x = 0 and x = L /3.

6. Some possibly useful integrals (not an exhaustive list!) You should be able to do “standard” integrals – polynomials, trig functions, exponentials