ConcepTest

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)
y(x)2) for some particle. You want
to determine the probability of finding the
particle in a region around some point x0. 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 y(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 2nd
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