“Test Your Knowledge”
Statistics
PROBLEM #1:
A particle is trapped in a 1-dimensional box of length L (infinite square well). The
particle acts inside the box as a free particle, but can not escape the box.
v
x=0
x=L
A.
Write the probability distribution function that describes the location of the
particle.
B.
What is the probability for finding the particle in the front half of the box?
C.
Calculate the average location of the particle for our 1-dimensional box.
D.
What is the standard deviation of the location of our particle in a box?
PROBLEM #2:
You are given a system where the location of the particle is a Gaussian centered
around x = 0. Thus, the probability distribution function is
Φ (x)  C ebx
A.
2
Determine the normalization constant C in our probability distribution function.
B.
Calculate the average location of the particle for our previous Gaussian
distribution system.
C.
What is the standard deviation for the location of a particle represented by our
Gaussian probability distribution function.
PROBLEM #3:
What is the probability distribution function for a particle trapped in a potential
1
2
well where V(x)  k x .
2