Quiz 3
Chem 3730
January 29, 2006
Answer all the questions below in the space provided. You may use maple to aid in your
analysis.
1) The kinetic energy for a particle moving in three dimensions is determined using the
operator:
p 2x  p 2y  p 2z
K
2m
The angular momentum operator is given by:
ˆ   yp  zp  ˆi   xp  zp  ˆj   xp  yp  kˆ
L
z
y
z
x
y
x
Therefore the x component is given by:
ˆ  yp  zp
L
x
z
y
a) Determine whether K commutes with Lx which is the x operator. (5 marks)
b) Using the above results comment on whether similar behavior is expected for Ly and
Lz and argue either that L commutes with K or not. (2marks)
2) A modified from of the 1D particle in the box equation ranging over 0 < x < 1 is given
as:
 ( x)  sin 5 x  exp 5( x  0.5) 2 
a) This wave equation is not normalized. Determine the normalization constant and state
the normalized form of the wave function. (show work)
(Hint: the expression looks a bit complicated. Don’t be intimidated! Just determine the
value using the evalf command). (5 marks)
See Maple file quiz3-2006
b) Plot and sketch the probability distribution of the particle as a function of x. (3 marks)
c) Determine the probability of finding the particle between 3/5 and 4/5. (5marks)
(show work)