# Third lecture advanced quantum mechanics

was a hard one. Today we have switched from "technical stuff" of second quantization to applications: Magnetism. Something about history of teaching attitudes. I have inherited this course years ago from prof. J.J.J. Kokkedee who gave it since 1970, I reckon. The latest "dictaat" of Kokkedee course can be found at the Blackboard. When inspecting this, one finds many similarities in contens. This is natural, because the fundametals of physics have not changed since that. What has changed is the teaching attitude and approach to student — taken the personal differences apart. Namely, the material of the lecture about magnetism was given to students at the exam: just a problem to solve. Modern education is decisively different. Roughly, the students of that time have been taught to less things, but have been expected to know more and to cope with more. A quick pseudo-logical conclusion would be: the students of the past were better prepared and in command of a superior intellengence. Let me say: negative, this is not so, in many cases it is (was) the opposite. Yet the further attempts to comprehend this would lead us to even more paradoxical conclusions, decisively more paradoxical than quantum concepts…

Back to the lecture. The timing was close to the ideal schedule: I was a bit double-crossing in the beginning when announcing the intention to finish the magnetism. Former experience shows that it could go worser: twice I was able to deliver only the second quantization for fermions. Today we stopped just on time: we have stumbled upon a technical problem discussing magnetism, got a prescription to deal with. Homework would do the rest.

Of course it was a bit too fast, I apologize. I hope you appreciate my good intentions. I was trying to tell about many things at once, my speech occasionally got erratic indicating the wandering mind. Must be irritating: Best way to stop it is to shoot a round of questions. Do me a favour.

Before the lecture got a question about my origin. In case more are interested: I was born in Siberia and dwell in the Netherlands since 1993, all time employed by TU. Suppose you like trains. Are you aware of possibility to travel from Amsterdam to Beijing changing trains just twice? If you take this challenge, you’ll pass my native city on the fourth day.

## 5 comments

:pLoved it, loved it, my first time here but won’t be the last. Keep the good work up.

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I definitely love reading your insight and learinig from your blogsite. Thank you for the interesting and informative article. – Pinoy

I don’t think it’s right to generalize to the conclusion that “in the past, students were smarter and knew more” from the observation that “we are now teaching in class what, in the past, students did on an exam.”

For one thing, you can just apply a parity operator to your middle step! What I mean is, you could say instead, “in the past, these problems came at the end of the course, with the exam: but now, these problems come at the very beginning of the course.” Then you get the result that students in the present are smarter than students in the past! Clearly, neither one is a good conclusion to draw from the observed fact.

The question for a lecturer today is, “what teaches the most to my students?” — and the students themselves have changed. In a world where *everyone* uses computers in their day-to-day lives, the *questions* that the people ask are different. And the big difference, I think, is that we ask what a method *does* rather than what it *is*.

An example is in order. You got this question in the lecture: “What happens when you apply the ‘n’ operator, which is a^T a, to the vacuum state?”

I think the best response for the student here is, “It does exactly what it should do. You get the eigenvalue — 0 — times the vacuum state. Because when you try to annihilate vacuum, the theory doesn’t support it — you just get a function which is 0 everywhere.”

This explains to the modern student what these n and a operators *do*, because explaining what they *are* is not sufficient for the modern sort of student.

In any case, the old style of teaching is not dead. 🙂 For my quantum mechanics class at Cornell University in the US, one quantum mechanics exam question, completely unexpected by the students, had an electromagnetic Hamiltonian. We were expected, with less than half a year of quantum mechanics:

(1) To see that the Hamiltonian contains E² and B² terms,

(2) To treat E and B as variables, so that this is a Hamiltonian for a 2D harmonic oscillator,

(3) To derive creation/annihilation “ladder” operators for E and B, like Griffiths did for harmonic oscillators,

(4) To come to the conclusion that the E and B fields themselves are quantized,

(5) And there was some problem at the end which became easy once you had the ladder, but I don’t remember the problem exactly any more.

Very few hints were provided; in particular, I was surprised on the exam to think of myself varying E and B for a field, rather than varying the position of a particle inside of that field. But they had the same expectation: by seeing how harmonic oscillator equations *are*, you should be able to figure out what they *do*.