Steven Kolaczkowski Time Independent Schrödinger Equation TISE and the Infinite Potential Well Free Particle solution if then our original harmonic wave solutions works and we can say You can verify that this will get us ID: 813122
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Slide1
Physics 214 HKN Final Exam Review Session
Steven Kolaczkowski
Slide2Time Independent Schrödinger Equation (TISE) and the Infinite Potential Well
Free Particle solution: if
, then our original harmonic wave solutions works and we can say
You can verify that this will get us Infinite Square Well: We need a function that is zero at x=0 and x=LFrom our options above, works if and is the state of the system and
Slide3Finite Potential Wells and Boundary Conditions
Normalization: since
is a probability density, the sum of all probabilities must be one
With changing potentials we force two boundary conditions to be met: and
Slide4Reflections and Tunneling
How does k change when we pass from a classically allowed region to a classically forbidden one? What happens when we go back?
Transmission Probability:
where , , and L is the thickness of the barrier
Slide5Time Dependent Schrödinger Equation (TDSE): dotting your
’s and crossing your
’s
TISE: Now we are going to look at time dependent wave functions TDSE: Superposition principle: TDSE can also be solved by:Notice that this is not a solution to TISE
Slide6Normalization and Orthogonality
Normalization:
Does this change with superposition? Will it change over time?
Orthogonality Principle:
Slide7Taking Quantum to Higher Dimensions
Wavefunctions still need to be normalized in all space.
In this class we will only deal with rectangular potentials or spherical potentials with no
dependence Want to see dependent potentials? Go to grad school!!!Hydrogen Atom Energy:
Slide8Quantum Numbers
(Principal):
describes the size of the orbital
(Angular or Orbital): describes the shape of the orbital (Magnetic): describes the orientation of the orbital
Slide9Spin and Moments
Stern-Gerlach: Electrons can only have two possible spin projections:
Slide10Classes of Particles and Beyond Hydrogen (
kinda
)
Fermions: half integer spinsCan NEVER share all the same quantum numbers (Pauli Exclusion Principle)Ex: electrons, quarks, protons, neutronsBosons: integer spinsPrefer to share all quantum numbers (This is the reason lasers work!)Ex: photons , gluons, pions, -particlesWant to learn more? Take Physics 470!!!For single electrons in atoms: where is the number of protons
Slide11Random Condensed Matter Topics
Molecular Potentials
Band Theory and Band Structure
Conduction and Valence BandsHow does Temperature affect electron transportWant to learn more? Take ECE 340 or PHYS 460 or I assume some Material Science class?
Slide12Exam Advice
Know when and how to use your equation sheet
Don’t panic, just keep on moving
Make sure you are in the right mindset going into the examSpend your time showing what you knowDON’T CHEAT
Slide13Past Exam Questions
Slide14Fall 2001
Slide15Fall 2001
Slide16Fall 2001
Slide17Fall 2001
Slide18Fall 2001
Slide19Fall 2001
Slide20Spring 2010
Slide21Spring 2010
Slide22Spring 2010 26 & 27
Slide23Spring 2010
Slide24Spring 2009
Slide25Spring 2010
Slide26Spring 2009