Working to Preserve, Promote and Advance Muskie and Pike Education and Research in Minnesota. December 1, 2014 Eightieth Edition From John Underhill, MMPA Co-chair The MN 2014 Muskie season is over but I hope it was a memorable one for you and your family. It was a very big year for Muskies and those of us who love to pursue and preserve them, with a 54-inch size limit coming for 2015 and discussions with the DNR about the future of Muskies and Pike being positive for anglers; we have much to look forward to. There is a problem in South Dakota; a group of sportsmen have petitioned the South Dakota Game, Fish and Parks to change the rules for spearing Game Fish to allow all species including Muskies. Please take time to send them your thoughts on protecting Muskies [email protected] The Hugh Becker Foundation recently awarded South Dakota Game, Fish and Parks $5,500.00 to upgrade equipment for their Muskie program. They state that there is no biological reason not to allow this even though it’s been researched to death and proven with the fish swimming in the water from Canada to MN and WI that protecting Muskies is the most valuable tool in the shed. Dead Muskies don’t give you the thrill of your life, as Jack Burns once said. They see it as a way to get a quick buck at the expense of the fishery, it’s easier to exploit it than to foster it and grow it into something lasting. We also have issues with Metro lakes under the threat of being shut down and unreasonably restricted, all are attempts to stop anglers from accessing the water while those who live there have unlimited access. The MNDNR has begun a new vetting process for the fisheries workshops with an application and term limits. This has some good elements but will potentially leave them with empty rooms in 3 years. When we attended the first one back in 2006 it had several purposes: create more Muskie fisheries, figure out what the problem with Pike was and if it could be fixed, and preserve all forms of fishing and harpooning. It got all of us
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Department of PhysicsUniversity of California
San Diego
Modern Physics (4E)Prof. V. Sharma
Final Exam(June 11, 2004)
Problem 1: Mystery Metal:[20 pts]Photons of wavelength 450nm are incident on a metal. The most energeticelectrons ejected from the metal are bent into a circular arc of radius 20cm ina magnetic field whose strength is equal to 2.0!10-5T. What is the workfunction of the metal?
Problem 2: Quantum Pool:[20 pts]An x-ray photon of wavelength 0.02480nm strikes a free stationary electron.The photon scatters off at 90o with respect to the direction of incidence.Determine (a) the momentum of the incident photon (b) the momentum ofthe scattered photon (c) the kinetic energy of the scattered electron, and (d)the wavelength of the scattered photon.
Problem 3: Across The Universe! :[20 pts]An air gun is used to shoot 1.0g particles at 100m/s through a bore (hole) ofdiameter 2.0mm. How far from the rifle must an observer be to see the beamspread by 1.0cm because of the uncertainty principle?
Problem 4: Harmonic Oscillator [30 pts]Consider a 3D harmonic oscillator, described by the potential
V (x, y, z) = 12m! 2 (x2 + y2 + z2 ) . (a) What is the energy of the ground state of
this system? What is the degeneracy of this energy? (b) Write down thewavefunction of the ground state. (c) Find the expectation value xyfor the ground state. (d) What is the energy of the first excited state? What isthe degeneracy of this energy?
Problem 5: Step On It: [30 pts]A free particle of mass m with wave number k1 is traveling to the right. Atx=0, the potential jumps from zero to V0 and remains at this value for
positive x. (a) If the total energy is E =!2k
12
2m= 2V
0, what is the wave number
k2 in the region x>0 ? (b) Calculate the transmission ( T ) coefficient at the
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potential step. (c) If 106 particles with wave number k1 are incident upon thepotential step, how many particles are expected to continue along thepositive x direction ? (d) How does your answer to part (c) compare with theclassical predictions?
Problem 6: Déjà vu: [30 pts]
Consider a particle in a 1-D Harmonic oscillator potential ( U (x) =
1
2m! 2x2 )
described initially by a wave that is a superposition of the ground state andthe first excited states of the oscillator: !(x,0) = C["
0(x) +"
1(x)] (a) show that
the value 1 / 2 normalizes this wavefunction assuming "1 and "2 arethemselves normalized. (b) Find the expression for !(x,t) at any later time t.(c) Show that the average energy in this state is the arithmetic mean
E
1+ E
2( ) / 2 of the ground state and the first excited state energies E1 and E2 .
(d) Show that the average particle position oscillates with time as
< x >= x0+ Acos(!t) where
x
0=
1
2x |!
0|2 dx +" x |!
1|2 dx"( ) and
A = x!
0*!
1" dx
and ! = E
2" E
1( ) / ! .
Problem 7: Lithium: The Musical! [30 pts]For the ground state of the Li++ ion, calculate the average (a) potentialenergy and (b) kinetic energy.
Problem 8: The Incredible Shrinking Atom:[20 pts]A collection of hydrogen atoms is placed in a 3.5 T magnetic field. Ignoringthe effects of spin, what are the possible wavelengths of photons emittedwhen an atom transitions from a 3s state to a 2p state?
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