Quantum Electronics

**Course Announcements in Reverse Chronological Order**

6/13 Letter grades are posted. I will circulate a memo regarding the final exam soon. I believe you don't feel intimidated with quantum math anymore. In your future study, perturbation, Fermi's golden rule, and density matrix theory, etc. will be quite useful, and you have studied all of them. Even if you "forget", you can "remember" quickly since your hands have permanent muscle memory. -TY

6/4 The density matrix theory problem needs some addition and correction as follows. -TY

**An off-diagonal matrix has all diagonal elements to be zero.**

(13) Show that d(ρ_{11} + ρ_{22})/dt = 0 and **d****ρ _{12}/dt = d**

(15) **Find out a general solution for Y.**

6/3 The final exam distributed.

This is EE232 final exam.

(1) Please scan your answer, compile images into **a single file**, and send it to me via email **by 11 pm. June 7 (Tue)**. If late, the same penalty rule as that for the midterm applies.

(2) Please confirm my **receipt**. I may request resubmission in case the file is not readable.

(3) If I find any typo, add comments, etc., I will post on **the course web**, so please check it everyday.

(4) I will scan week 10 notes and post it tonight.

Some questions are discussed in class, and some may be new and tough. I hope you will learn Quantum Electronics more in solving these questions and that's the entire purpose of doing this final exam.

Cheers,

-TY

5/31 The final take-home exam schedule is similar to that of the midterm. Exam distribution on 6/3 (Fri) and submission by 11 pm on 6/7 (Tue). -TY

5/31 HW5 sol uploaded. We will not meet on 6/2 (Thu), but I will be at UCSC. If you have any questions, come to E2 247A during 4-6 pm. -TY

5/28 We have discussed the difference between the E-feild and D-field. Contrary to common believe, the D field is the input and the E-field is the output. The transfer function is 1/ε rather than ε. This is critical in understanding screening or schielding, which is often misunderstood. -TY

5/28 class notes week 9 posted. -TY

5/26 **HW5 due on 5/31 (Tue)** posted. HW3 sol posted. HW4 sol will be posted tonight. -TY

5/18 **HW4 due on 5/26** **(Thu)** posted. -TY

5/18 Another "editorial" comment after grading. Some people's scan is very **hard to read**. Please improve it in the final exam if you are warned this time. Many people wrote more than necessary, and it degraded readability. This is critical in communication with referees when you submit a paper to a peer-reviewed journal. You must **write sufficient and enough**. Finding the exact balance is not easy, but you can always ask yourself, is my writing easy to read? -TY

5/18 The midterm grading is complete.** Over all, you did well.** You will be getting scanned graded exams **tonight**. In the time dependent perturbation, finding out a_{k}^{(1)} is only an intermediate stage. You need to integrate its magnitude square with respect to angular frequency ω. The physical meaning of this process is to shake the unknown box with various ω and let the system choose the most favorite ω. Then you will be getting a transition probability proportional to the time duration. You must normalize it to that per time. Another thing. Many people had trouble with bracket math with ∑, and you want to be familiar with it. I hope that you feel more comfortable with math after being exposed to the density matrix theory. -TY

5/12 We are finishing the Fermi's golden rule and moving to the density matrix theory. -TY

5/10 Fermions (e.g., electrons) and Bosons (e.g., photons, Cooper pairs) are discussed. -TY

5/7 Small correction for P5. **Unlike P3 or P4, we want to keep ω as a variable. Please discuss the transition scenarios depending on the ω values in P5 of H'(t) = γx ^{2}[exp(iωt)+exp(-iωt)].** -TY

5/6 Typo in P1. Vector potential **A** = (-yB,0,0) and q is unnecessary. Sorry for that. -TY

5/6 The ee232 take-home **midterm had just been sent out** at 11:40 am today. Please make sure you have it. **The submission deadline is 11 pm on May 10th (Tue)**. Good luck. We will have a regular class on that day. -TY

5/5 The take-home midterm distribution via email is scheduled to be **Friday morning, May 6th**. If there is any change for this schedule, I will let you know. Please check this web site regularly. After the distribuition is announced, if you don't receive anything, please let me know immediately. -TY

5/4 HW4 will be assigned after the midterm. -TY

5/3 We have seen DOS behavirs in various dimention, various dispersion cases.

4/26 We are examining time-dependent perturbation theory. In the Fermi's golden rule, DOS is introduced, which is converted to count in k-space. -TY

4/22 Week 4 class notes uploaded. --TY

4/22 We want to **schedule a midterm**. It will be a take-home exam, and the candidate week is the first week of May. I am thinking of 5/6 (Fri) exam distribution and 5/9 (Mon) or 5/10 (Tue) submission, but it is possible to avoid the weekend, if you want. Let us finalize the schedule in the next class. If you have any personal preference/schedule conflict, please let me know. -TY

4/21 We have studied 1st and 2nd order perturbation theory amd examined two exactly solvable examples to perturbation. They are consistent and our sanity check has complete. We will move to time-dependent perturbation next week. -TY

4/20 Just in case, previous lecture videos can be found at **here**. -TY

4/19 HW2 sol and **HW3 due on 4/26 (Tue)** are posted. We are continuing perturbation theory. -TY

4/17 It is always a good idea to summarize a logical flow after detailed math derivations. Due to comlicated math, we very often get lost. If you can summarize the logical flow, you should feel confident, and that will constitute your strong technical background. -TY

4/16 Landau quantization is a very good example for a quantum harmonic oscillator system. The classical Hamilton equation of motion recovers the Lorents force, and replacement from p to p - qA under the B-feild is justified. Then the Schrodinger equation is reduced to that of a harminoc oscillator and energy levgels are quantized as hω (n + 1/2). Simultaneously, we have started studying the perturbation theory.

4/15 Class notes for weeks 2 and 3 are posted. -TY

4/14 We have discussed time-independent and time-dependent purterbation examples. Tomorrow, I will post the class notes so far. -TY

4/13 HW1 sol and **HW2 due on 4/19 (Tue)** posted. A pdf version is also posted. -TY

4/13 The SVC location is changing permanently. Apr 14 (Thu) at 4 pm is the last meet at the old place. **3175 Bowers Ave** is the new place starting on Monday, Apr 18 at 8 am. The classroom information is still not in the public domain. I was advised that we need to ask at the front desk and they will give us the exact information on Tuesday afternoon, before our class starts. You can call 408-861-3700 or email to extensionprogram@ucsc.edu for more information. -TY

4/13 We have studied Landau level formation using quantum. We have also seen the matrix treatment of harmonic scillators. They are all important and please review. -TY

4/11 We have seen that the harmonoc oscillator Hamiltonian normalized to hω is H = (a^{+}a + 1/2), where a^{+}a, number operator, is a diagonal matrix whose elements are 0, 1, 2, 3, ... etc. The eigneenergies are shown immediately n + 1/2. The matrix formalism is in a sense much more direct than the differential formalism of Gauss function x Hermite polynomial. -TY

4/5 ee232_memo_4-5-2016 for Hermite correcting typos uploaded. **HW1 due on 4/12 (Tue). Sorry for the typo, that is due on Tuesday, 4/12. **Please scan your answer and send me via email. Please use a low but readable resolution (please limit to a few Mb). -TY

4/4 Class note for week 1 uploaded. -TY

3/30 We have started EE232. Please log in and make sure you have an access for this page. We will punctually derive all equations, and establish strong background for quantum. -TY

**EE232 Quantum Electronics Spring 2016 Course Preface**

Basic quantum mechanics is reviewed and it is applied to the study of interactions between light and materials. Quantum theory often ends up with a lot of integrations, and we may unfortunately get lost in mathematics, but quite often, mathematics is left as our exercise. Also detailed calculations start without clearly identifying what the initial problem is. Thus, we will make every effort to (1) derive all mathematics in class, (2) identify the logical flow, and (3) create clear mental images for or visualize topics we study in EE232. Lasers and light-matter interactions will be mainly covered, but whenever there is a conflict between understanding well and covering widely, we will choose the former.

We will use A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989). This is not an easy book to study as you can tell from customer reviews, and we will fill the gap in class, i.e., derive all mathematics and clarify the logoical flow. The midterm (35 %) and final exams (55 %) are planned. HW (10 %) will be assigned every week, and is basically a review of what we cover in class from a different angle.

***Important**** Please click Class Guide (Secure) regularly with your BlueCruz ID, since all important communications are posted there. HWs and class notes are posted in Attachments, but again you need your BlueCruz ID.

If you have trouble in logging in, please contact the IT Dept. There was a suggestion that clicking "Join class" at first would be a solution. I still do not see all registered people for this web site members' list. Please log in, otherwise, you will not see HW1 or class notes forever.

Toshishige Yamada, Ph.D. (EE)

山田俊茂 工学博士

http://users.soe.ucsc.edu/~tyamada

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