Physics 3220 – Quantum Mechanics 1 – Fall 2008
Problem Set #8
Due Wednesday, Oct 22 at 2pm
Problem
8. 1
Review – with some realistic numbers [
15 pts]
A CO (carbon monoxide) molecule can be modeled as a vibrating spring. When you have
two
objects
("C" and "O" here) it might seem to be a different problem than what we've studied this term, but we
will show later this semester that, like in classical physics, you can consider this system to be
equivalent
to a
single
object with a reduced mass
μ
1/(1/
m
1
+1/
m
2
)
, vibrating like a simple 1D harmonic
oscillator. CO molecules absorb and emit radiation at a wavelength of 47,000 Angstroms. (This is in the
IR) This corresponds to excitation (or radiation) of this harmonic oscillator system with a change of the
quantum number
∆
n=1. Use the above information to deduce the "spring constant", k, between the "C"
and "O" atoms in this molecule in MKS units.
(M(Carbon)=12 amu, M(Oxygen)=16 amu)
(Note that
typical, everyday springs have k’s of order 100’s to 1000’s of N/m. Does your “quantum k” surprise you at all?)
At room temperature, do you think CO molecules will generally be in their vibrational ground state, or
some thermal distribution that would include many excited states? (Why?)
Problem
8. 2
Is it a vector?
[15 pts]
All the parts in this question refer to vector spaces.
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 Fall '08
 STEVEPOLLOCK
 mechanics, Hilbert space, Hermitian Operators, Hermitian conjugate

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