Week 15

Current and upcoming hw assignments

Ch. 14    4, 6, 9, 12, 13, 16, 19, --- Wed. April 15

Ch. 15 Assignment        5, 9, 18, (on 18 B make that sketch a plot NOT SOME HAND DRAWN THING---users choice of software). Due April 22 or thereabouts

• Comments in general:

  Schroedinger's equation is a wave equation.

• When the Energy is greater than potential E>V, then solutions look like
• WAVES----That is (exp(ikx))---we know how to put in the time part for each value of k
  • We may be able to add many different values of k (energies) so that we get some kind of modulated wave--think Fourier series.
  • The exp(ikx) can always be expressed in terms of sin, cos, or their series'sss (and includes exp(-ikx), wave either way).
• For the case with E<V we should get solutions that (YES, that is negative KE??? ).
  • Exp(kappa*x). Where kappa plays a "k" like role to avoid the square root of negative which we already took out and multiplied by the existing "i" in the last oscillation solution.
  • These solutions look like exponential growths or decays.
• Aside from some superposition, adding, etc _--which can always lead to arbitrarily wonky looking functions----the SOLUTIONS TO WAVE EQUATIONS WILL GENERALLY APPEARS AS EITHER OF THE TWO THINGS ABOVE (WAVES, OR GROWTH/DECAY). Sometimes there is some geometry to contend with (space is 3 dim).
• I may give other psi for exercise of normalizing---or whatever (grinding math)----but wave equations have a type of solution that you should be on the lookout for.
• Normalization must also be answered to.
• Your wavefunctions should not grow to infinity as x gets large. Boundaries exist. Boundary condiitions exist.
• Wavefunctions that become infinite and infinite number of times in a small region can also be difficult to deal with.
• Sometimes reality will really limit what math we can write out.

Future, we'll get through 13, 14, 15 (quantum intro) and a little bit more.

Exam 3, Chs.  ~10-15+ Monday April 20th note the Monday

• Things to know
  • Energy levels for Hydrogen(Like) atoms (formula)
  • Time dep and indep S.W.E. (formula)
  • Energy levels and wavefunctions for infinite square well(s)---the equations/formula
• How to normalize a given wavefunction (definitely know this 100%), and how to find probability given a wavefunction (you should probably know this). --set it up.
• Changes in Hydrogen due to reduced mass compared to not reduced mass or vice versa. KNOW WHICH ATOMS ARE MORE REDUCED MASS LIKE AND WHICH ARE MORE INFINITE MASS LIKE!!!!!!!!!!! ---qualitative.
• Finite square well bound states--consider changing -----qualitative
  • Height of well
  • width of well
  • compare to infinite well
  • be able to sketch wavefunction details.----
• Infinite square well
  • Use wavefunctions to find probability
  • Average of a quantity (expectation value)
• Given Hydrogen Like atom-
  • find energies
  • transition wavelengths
  • Radius of given orbits

We will discuss some "additional topics" in quantum mechanics.

In the time remaining we may discuss (will continue)

• Sloshing States
• Comparison of Classical and Quantum Simple Harm. Osc.
• Lasers
• I'll be posting some notes on angular momentum and magnetic dipole moments

Final Exam Comments: Coming ASAP

• Relativity---
  • length or time transforms or contraction and dilation
  • angle
  • mass
  • blackbody peak and Doppler shift
• Blackbody
  • Peak wavelength and frequency
  • Power output
• Energy, Electrons, Photons
  • Speed of electrons moving relativistically
  • braking radiation
  • Compton scattering
• Light
  • Absorption coefficient
  • Changed absorption conditions
• Hydrogen ignition / emission
  • Energies
  • Transition
  • frequency of each wavefunction
• A particle stuck in a well
  • Time dep solutions
  • probability density with time dep
  • sloshing frequency
  • expectation value

• And here is a top 10-ish movie list---(I omit various eye candy and fantasy style movies, .....musicals.....? ).

Many of these are character development drama's

In no particular order

• Apocalypse Now (is simply the best made movie ever---NOT THE REDUX VERSION---NO--The original theater release only. The cast! )
• Inglorious Basterds (and note the misspelling deliberately in the title)
• Casablanca ("Here's looking at you kid", "we'll always have Paris", " I think this is the beginning of a beautiful friendship")
• Judgement at Nuremberg (and many other Spencer Tracy like Boys town--though you will find dated)
• Butch Cassidy and the Sundance Kid (or other Paul Newman movies like the Sting, Cool Hand Luke, or Cat on a hot.....)
• Little Big Man (the most under rated great movie of all time---Dustin Hoffman at his best---well---and Marathon Man)
• The Princess Bride (C'mon---you will all have your kids watch this one, over and over -----my name is Inigo Mantoya. You killed my father. Prepare to die)
• The Magnificent Seven ( the 60's version---not remake---maybe you like the Seven Samurai--OK. Again the cast)
• A wonderful life (and many other Jimmy Stewart--Harvey, The man who shot liberty valence, and others)
• The Godfather ( I had to include Marlon Brando----On the waterfront is better, but The Godfather is his signature movie, and superman 1978, )
• Lawrence of Arabia
• One Flew Over the Cuckoo's Nest (Best book to movie adoption of all time---and the book was written on ........well maybe that is a myth, but who knew that Nurse Ratched would show up on Deep Space 9--and playing darn near the same character).
• 12 Angry Men
• Amelie
• And there are so many other meritorious---but many of these are tops.