## Physics 3220: Quantum 1

### Week 17

Final Exam solutions are available on D2L. Scores are posted on D2L.

The exam generally went well. Average: 80 +/- 15 of 100 points total. See Exams tab for a histogram.

All HW scores are uploaded. Please double check your scores ASAP.

__Reading__: You're the boss now, but I'd read the rest of Griffiths,

or even better, get out that copy of Shankar are start reading.

__Homework__: None, you're done!

### Week 16

In this final week of the course, we will cover addition of angular momentum,

and what to do if you have when there are more than a single particle

in the quantum mechanical system of interest. You will develop these ideas

in the second semester, but we should be able to begin discussing quantum

entangled states by the end of the week.

**Final Exam is Monday Dec. 17 4:30P-7P, in Duane G-125.**

__Reading__: Griffiths Chapters 1-4 again in review for the final exam.

__Homework__: HW14 is due Friday Dec. 14 in class. For EXTRA CREDIT, you can

also do the Schroedinger's Mouse tutorial due Mon. Dec. 17, by 12noon in my mailbox.

### Week 15

Spin 1/2 intrinsic angular momentum and the analogy to two-level systems

will be the major topic this week. The Hilbert space is only two-dimensional

but displays all the things we've seen in quantum mechanics (hermitian ops that

might or might not communte, uncertainty principal behavior, etc.) but without

any differential representations.

__Reading__: Griffiths Chapter 4.4.3 on addition of angular momentum

__Homework__: HW13 is due Friday Dec. 7 in class.

### Week 14

Now that we have solved for the energy eigenstates of the hydrogen atom,

we can investigate the predictions that come from these solutions and their

linear superpositions. Due to energy degeneracy, the stationary states are

more complicated and the linear superpositions display interesting beat frequencies.

We will also begin our investigation of the angular momentum operators and spin.

__Reading__: Griffiths Chapter 4.

__Homework__: HW12 is due Friday Nov. 30 in class.

### Week 13

Enjoy the Thankgiving Break.

__Reading__: Griffiths Chapter 4.

__Homework__: No HW over break. HW12 will be due Friday Nov. 30 in class.

### Week 12

Exam 2 solutions and scores are on D2L. Exam 2 histogram is on the Exam page.

This week we will move through the spherical harmonics for central potentials

on to the solution of the radial equation for the hydrogen atom.

The hydrogen solution is our first realistic 3D case. Outstanding!

__Reading__: Griffiths Chapter 4.

__Homework__: HW 11 is due Friday Nov. 16 in class.

### Week 11

Exam 2 solutions are also on the Exam page.

This week we will move to solving the S. E. in spherical coordinates and

Begin the treatment of the hydrogen atom. Orbital angular momentum appears!

Also, Exam 2 is Thursday evening, Nov. 8 from 7:30P to 9P in BESC 180.

__Reading__: Griffiths Chapter 4.

__Homework__: HW 10 short HW is due Friday Nov. 9 in class.

### Week 10

Back to doing quantum mechanics in the position representation again!

We are now going to go back to doing QM problems, but now in more than 1D.

Try your best not to forget the general structure and bra-ket notation. It's

very useful for helping to push through the more complicated aspects of

these new and messier problems.

__Reading__: Griffiths Chapter 4.

__Homework__: HW 9 is due Friday Nov. 2 in class.

### Week 9

Hermitian operators and their properties are especially interesting....

Many of the things that you've seen with solutions to the Schrodinger Eq.

(real-valued eigen energies and othonormal eigen functions) are general

for Hermitian operators. The Sch. Eq. is an important special case of the

an eigen value equation for a Hermitian operator (the energy operator).

__Reading__: Finish Griffiths Chapter 3 and start Chapter 4.

__Homework__: HW 8 is due Friday Oct. 26 in class.

### Week 8

This week we will begin circle back to the beginning of the course and

discuss the general structure of quantum mechanics: Wave functions

are vectors in a complex Hilbert space, operators transform initial

vectors to new vectors. Hermitian operators are especially interesting....

__Reading__: Griffiths Chapter 3.

__Homework__: HW 7 is due Friday Oct. 19 in class.

### Week 7

Piece-wise flat potentials let us build finite-depth potential wells, tunneling barriers, and

provide us with model solutions that are used regularly in physics and chemistry. We'll concentrate

on the finite potential well and the barrier transmission problem this week.

__Reading__: Griffiths Chapter 3.

__Homework__: HW 6 is due Friday Oct. 12 in class.

### Week 6

**Exam 1 is complete. Solutions on D2L**.

Last week we learned about operator methods, a new way to do quantum mechanics. In the operator method,

what matters most are the COMMUTATION RELATIONS between operators, in other words, the rules of the non-

commuting algebra, not the partcular REPRESENTATION of the operators. It matters that [x,p]=ihbar, not

that p = hbar/i d/dx. This week we continue to play in the operator sandbox and return again to cover

the free particle, with an eye on learning the MOMENTUM REPRESENTATION, a third way to do quantum mechancis.

__Reading__: Griffiths Chapter 2.6 on finite potential well. Start Chapter 3.

__Homework__: HW 5 is due Friday Oct. 5 in class.

### Week 5

**Exam 1 is Thursday evening, 7:30P-9P in
Benson Earth Sciences BESC 180**.

This week we will cover the 'operator algebra' approach to solving the harmonic oscillator problem.

__Reading__: Griffiths Chapter 2.4, 2.5, and 2.6 on the free particle and finite potential well.

__Homework__: HW 4 short assignment is due Friday Sept 28 in class.

### Week 4

We continue studying 1-d quantum systems. This week we cover the harmonic oscillator by two different approaches. First, we solve the time-independent S.E. eigenengeries and wave functions. Second, we will see our first example of 'operator algebra' solutions. This second approach shows you that you do NOT need to solve a partical differential S. E. do do quantum mechanics. This approach is decended from Heisenberg's Matrix Mechanics, an alternative way to solve quantum problems and still the way quantum field theory is done.

__Reading__: Griffiths Chapter 2.3, 2.4, and 2.5

__Homework__: HW 3 is due Friday Sept 21 in class.

### Week 3

We are starting into Chapter 2, 1-d Quantum Mechanics and the time-independent Schrodinger Equation. We will solve a number of the important 1-dimensional problems e.g., the infinite square well and the harmonic oscillator. We will find a number of special wave functions. REMEMBER: The general wave function is always a linear superposition of these special wave functions.

__Reading__: Griffiths Chapter 2.1 and 2.2

__Homework__: HW 2 is due Friday Sept 14 in class.

### Week 2

No lecture on Monday, Sept. 3, for Labor Day.

Have a look at the course syllabus

__Reading__: Finish reading Appendix A on linear algebra and Chapter 1. Start Chapt. 2.

__Homework__: HW 1 is due Friday Sept 7 in class.

### Week 1

First lecture is Monday, Aug 27, 2:00P-2:50P, in room Duane G125.

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.), and consider buying the additional text by Shankar.
Buy a clicker if you donâ€™t have one already. Follow the instructions on MyCUInfo for registering the clicker.

__Reading__: Start reading Appendix A on linear algebra, and Chapters 1, and 2.

__Homework__: None assigned yet.