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Physics 214  HKN Final Exam Review Session Physics 214  HKN Final Exam Review Session

Physics 214 HKN Final Exam Review Session - PowerPoint Presentation

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Physics 214 HKN Final Exam Review Session - PPT Presentation

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

energy spring wavefunctions time spring energy time wavefunctions superposition momentum eigenstate tdse principle 2018 practice equation tise quantity exam

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Slide1

Physics 214 HKN Final Exam Review Session

Steven Kolaczkowski

Slide2

Wavefunctions 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

 

Slide3

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: 

Slide4

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 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

 

Slide5

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

 

Slide6

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?

 

Slide7

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

Slide8

Exam 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

Slide9

Past Exam Questions

Slide10

Spring 2018 Practice

Slide11

Spring 2018 Practice

Slide12

Spring 2018 Practice

Slide13

Fall 2001

Slide14

Spring 2009

Slide15

Spring 2010

Slide16

Spring 2010