# Time Dependent Perturbation Theory Homework

Pictures of 1, 2, 3, 6, and 12 magnesium ions held in a linear Paul trap at NIST, as reported in the 30 June 2006 Physical Review Letters. Quantum systems often contain many interacting particles. In this course, we will discuss how to think about and describe complicated quantum systems, where exact solutions are usually not available.

### Finals Week

Congratulations on completing Physics 4410 Quantum Mechanics and Atomic Physics 2 Letter grades are posted. Your take-home Final Exam scores are posted on D2L along with solutions to the take-home Final Exam. All your HWK reworks are scored and feedback is posted on D2L. Please look at the scores and look for any factual errors.

Also posted are 'proto-Letter' grades that will become the final letter grades by Sunday May 8.

__Reading__: Enjoy a good book.

__Homework__: HWK is finished for the term.

### Finals Week

Your take-home Final Exam is posted on D2L. Your final exam written work is due no later than Thursday May 5, 10PM. Feel free to turn it in early in my mailbox, as per the instructions on the exam. HWK reworks are due Monday May 2 late evening. The final is open book and you are encouraged to cross-check your work with colleagues. The final could have been a normal 2.5 hour exam, so be sure that you give it only the time that is justified. No lectures this week, but the Monday HWK session will take place as usual.

Homework sessions are in Duane G131. Monday this week, 4:00-6P

__Reading__: Griffiths Chapter 12 on quantum entanglment and Bell States.

__Homework__: HWK Rework due Mon., May 2, 2016.

### Week 16

This week we will continue with discussion of quantum computation and quantum information processing. Many of the things that you've learned about atomic physics, preparing states, and evolving them with time-dependent potentials are exactly the type of things you need to know to build quantum logic gates.

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Griffiths Chapter 12 on quantum entanglment and Bell States.

__Homework__: HWK Rework due Mon., May 2, 2016.

__Homework__: HWK 12 due Wed., April 27, 2016.

### Week 15

Now that we understand how to drive transitions between different energy-levels, we can begin doing quantum manipulation of things like atoms, nuclear or electronic spins, or any other system one is interested in. Increasingly, we have learned how to do these manipulations on individual atoms, ions, etc. and we are beginning to build machines that behave genuiuely quantum mechanically. This week we will begin looking at efforts to build 'quantum computers'. These machines may be the future of computer technology.

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Griffiths Chapter 12 on quantum entanglment and Bell States.

__Homework__: HWK Rework due Mon., May 2, 2016.

__Homework__: HWK 12 due Wed., April 27, 2016.

### Week 14

We are continuing with our study of time-dependent Hamiltonians. Finally! We can study systems where the populations in different basis states can change with time. You are now in a position to understand how applied electric and magnetic fields can drive transitions between different quantum states. Excellent!

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Griffiths Chapter 9 on Time-dependent perturbation theory.

__Homework__: HWK 11 due Wed., April 13, 2016.

### Week 13

We are continuing with our study of time-dependent Hamiltonians. Finally! We can study systems where the populations in different basis states can change with time. You are now in a position to understand how applied electric and magnetic fields can drive transitions between different quantum states. Excellent!

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Griffiths Chapter 9 on Time-dependent perturbation theory.

__Homework__: HWK 11 due Wed., April 13, 2016.

### Week 12

Welcome back from Spring Break.

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Griffiths Chapter 9 on Time-dependent perturbation theory.

__Homework__: HWK 9 due AFTER Spring Break on Fri., April 1, 2016.__Homework__: HWK 10 due Wed., April 6, 2016.

### Week 11 Spring Break

Enjoy your Spring Break!

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Griffiths Chapter 7 on Variational Method, and Chapter 5.2 on Atoms

__Homework__: HWK 9 due AFTER Spring Break on Fri., April 1, 2016.

### Week 10

**Exam scores and histogram on D2L.**

The electrons in atoms are Fermions and must be in a state vector of anti-symmetry overall in electron exchange. State vectors with anti-symmetric spatial parts keep the electrons further apart, lower the overall energy, and result in correlated spin properties in the atoms of the Periodic Table. We will concentrate on atoms in the Periodic Table.

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Griffiths Chapter 7 on Variational Method, and Chapter 5.2 on Atoms

__Homework__: HWK 8 due AFTER mid-term exam on Wed., March 16, 2016.

### Week 9

**Mid-term Exam on Thursday, March 10, 7:30-9P in Duane G130.**

The Variational Method provides us with a way to search for approximate ground state energy eigen values and approximate ground state eigen state vectors by artistically guessing! Insight about possible properties of multi-particle systems can be built into state vector guesses and then tested by expectation value of the Hamiltonian to place an upper-bound on the ground state energy. Many of the most important insights into many-particle systems were produced by using the Variational Method. These include understanding the Periodic Table via variational states for multi-electron atoms, the Bardeen-Cooper-Schrieffer theory of superconductivity, the Laughlin states for the fractional quantum hall effect, and many others. We will concentrate on Helium and other atoms in the Periodic Table.

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Griffiths Chapter 7 on Variational Method, and Chapter 5.2 on Atoms

__Homework__: HWK 8 due AFTER mid-term exam on Wed., March 16, 2016.

### Week 8

This week we start coverage of multi-electron atoms by introducing the symmetric (Bosons) and anti-symmetric (Fermions,) with respect to exchange of particle, state vectors that nature requires for identical particles. We then begin discussing the case of the Helium atom.

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Review Griffiths Chapter 5 and Chapter 7

__Homework__: HWK 7 due on Wed., March 2, 2016.

### Week 7

Fine and hyper-fine structure of hydrogen and the beginning of multi-particle systems are the topics this week.

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Review Griffiths Chapter 6 and Chapter 5

__Homework__: HWK 7 due on Wed., March 2, 2016.

### Week 6

We are considering the fine structure of the observed energy eigen-values of hydrogen. The predicted energy eigen-values that come from the Schroedinger Equation treatment that we saw last semester are very close to the observed values, but are not exactly as observed. There are small deviations between the simple predictions and observations that arise from relativistic effects and from the small contributions due to magnetic fields and spin. Perturbation theory provides a way to predict the size of these small energy shifts.

Homework sessions are now in Duane G131. Monday 4:30-6P and Friday 4-6P

__Reading__: Review Griffiths Chapter 6.

__Homework__: HWK 6 due on Wed., Feb. 24, 2016.

### Week 5

We continue our treatment of time-independent perturbation theory with both degenerate and non-degenerate cases. With these techniques, we'll start considering the fine structure of the observed energy eigen-values of hydrogen.

Homework sessions are now in Duane G131. Monday 5-6P and Friday 4-6P

__Reading__: Review Griffiths Chapter 6.

__Homework__: HWK 5 due on Wed., Feb. 17, 2016.

### Week 4

This week we will start covering Griffiths Chapter 6 material on dealing with Time Independent Perturbation Theory. The topic is how to produce approximate solutions for the eigen state vectors and eigen energies for systems that we cannot solve exactly, but which at least have time-independent Hamiltonians.

Homework sessions are now in Duane G131. Monday 5-6P and Friday 4-5:30P

__Reading__: Review Griffiths Chapter 6.

__Homework__: HWK 4 due on Wed., Feb. 10, 2016.

### Week 3

We have reviewed spin 1/2 systems and a composit system with a pair of spin 1/2 objects. For example, the hydrogen atom has a spin 1/2 nucleus and a spin 1/2 electron. This week, we will move to studying the polarization states of light. The photon behaves like a two-level system because it can have two orthogonal polarization states. It's a two-state system!

Homework sessions are now in Duane G131. Monday 5-6P and Friday 4-5:30P

__Reading__: Review Griffiths Chapters 1-4.

__Homework__: HWK 3 due on Wed., Feb. 3, 2016.

### Welcome to Physics 4410! Week 1 and Week 2

First lecture is Monday, Jan. 11, 2:00P-2:50P, in room Duane G131.

Have a look at the course syllabus

__Summary of things to do during or by the first week__:

Buy the text (David Griffiths's Introduction to Quantum Mechanics, 2nd Ed.).

Buy a clicker if you don't have one. Then follow these instructions to register.

__Reading__: Review Griffiths Chapters 1-4.

__Homework__: HWK 1 due on Friday, Jan. 22, 2016.

The syllabus provides a complete schedule for the course and access to all the web-based material. Click on the appropriate document below to get a pdf file for lecture notes, special handouts, homework assignments, challenge problems, exams, and solution sets. The two rightmost columns below give the relevant sections of the main textbook and of the additional texts that are available for review and perspective.

Objectives, Content, Pedagogy, Methods of Evaluation, and Policies: You should read this pdf document carefully at the beginning of the course and consult it whenever you have questions about how the course is administered.