Steven Kolaczkowski Wavefunctions and Eigenstates Wavefunctions are how we describe the probabilistic nature of quantum particles By themselves wavefunctions do not have an intuitive meaning ID: 800816
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Slide1
Physics 214 HKN Final Exam Review Session
Steven Kolaczkowski
Slide2Wavefunctions and Eigenstates
Wavefunctions,
, are how we describe the probabilistic nature of quantum particles. By themselves, wavefunctions do not have an intuitive meaning.
iff Momentum of a particle is described by its wavenumber, In later classes, , will be a vectorWhen we say a wavefunction is an eigenstate of some quantity, we mean that quantity is definite.Ex. is a momentum eigenstate with momentum is an eigenstate of both momentum and energy
Superposition, Normalization, and Orthogonality
Superposition: If we have two valid wavefunctions, linear combinations of these wavefunctions are also valid.
If a wavefunction is a superposition of a quantity (momentum, energy, polarization, etc.) it is
not an eigenstate of that quantityNormalization:Does this change with superposition?Orthogonality Principle:
Slide4Time 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
Finite Potential Wells, Boundary Conditions, and Harmonic Oscillators
With changing potentials we force two boundary conditions to be met:
and
Harmonic Oscillators have potentials, and have their energy states described by
Time 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
Superpositions oscillate with a beat frequency
Does
vary with time?
Band Structure and Intro to Condensed Matter
Pauli Exclusion Principle: For this class, all it means is you can have a max of
2
electrons per energy level.When independent materials are brought together, their shared energy levels split into bonding and anti-bonding state.Bandgap: The separation between energy levels in a material. There are no available states for particles to fill in the gap.Metals have no bandgapInsulators have large bandgapsSemiconductors have small bandgapsWhat constitutes large and small? Pft. Nothing really
Slide8Exam 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
Slide9Past Exam Questions
Slide10Spring 2018 Practice
Slide11Spring 2018 Practice
Slide12Spring 2018 Practice
Slide13Fall 2001
Slide14Spring 2009
Slide15Spring 2010
Slide16Spring 2010