This preview shows pages 1–2. Sign up to view the full content.
Chemistry 120A
Spring Semester, 2009.
Problem Set 2
Due Fri. Feb. 6, 2009.
1.
Another particle in a box problem.
Suppose that a particle in a box (of length
L
) is
represented at an instant in time by a state
!
with wavefunction:
x
( ) =
Nx
2
L
2
"
x
2
( )
(a)
Evaluate the normalization constant,
N
, such that
x
( )
is normalized (i.e.
=
1
)
(b)
Evaluate the average energy which would be obtained by making measurements on
a very large number of identically prepared systems using the expectation value
expression,
E
=
ˆ
H
, for normalized wavefunctions.
2.
A followon to “Another particle in a box problem”.
Same particle in the same box, in
the same state,
:
(a)
A very natural basis in which to represent
=
"
j
c
j
j
#
is the basis of energy
eigenfunctions,
n
where
n
is the quantum number.
Evaluate the first few
expansion coefficients (
c
n
=1
,
c
n
=2
,
c
n
=3
,
c
n
=4
) explicitly.
(b)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/22/2010 for the course CHEM N/A taught by Professor Headgordon during the Spring '09 term at University of California, Berkeley.
 Spring '09
 HEADGORDON

Click to edit the document details