Contemporary Physics I – HW 8
HW 8
Due November 30, 2007
Note the 2 week due date
Please answer all questions clearly and concisely. While you need not transcribe the question
completely, it should be clear from your answer alone what you are talking about.
You are strongly encouraged to discuss the homework with your classmates, but you must complete
the written homework by yourself, and of course, the material you submit must be your own.
Remember, show all of your work!
1. Compute the DeBroglie wavelength of the following
(a) An electron traveling at 20m/s
(b) A 70 kg human with a kinetic energy of 8000 J.
(c) A proton with γ= 2.5.
2. You observe three (non-interacting) particles with:
m1=1 kg, m2=2 kg, and m3=3 kg, and at positions:
~r1=<2,1,0> m,~r2=<−4,2,0> m,~r3=<1,0,0> m, and with velocities:
~v1=<3,0,0> m/s,~v2=<−2,2,0> m/s,~v3=<−1,3,0> m/s.
(a) Where is the center of mass? (I’m looking for a vector.)
(b) What is the center of mass velocity?
(c) What is the translational kinetic energy?
(d) What is the total energy of the system (not including mass energy)?
3. Consider a wave with a wavelength λ= 500nm, and a propagation speed 3 ×108m/s (you
may know this as c).
(a) What is the wavenumber of wave (k)?
(b) What is the frequency of oscillations (ν)?
(c) If the wave is a lightwave, at what energy is it?
(d) What is the momentum of the corresponding photon?
4. A quantum mechanical particle is in the following potential:
U(x) = 1
2mω2x2
(You may recognize this as a simple way of re-writing the energy of a harmonic oscillator). I
assert to you that the Schroedinger Wave Equation:
−¯h2
2m
d2ψ
dx2= (E−U(x))ψ
can be solved in the ground state as:
ψ(x) = ψ0exp(−x2/2σ2)
