[saito200]

Hi everyone,

I'll soon be teaching quantum chemistry privately, and I'd like to ask you:
When you took your first course about quantum mechanics: Did you find something about the subject particularly difficult? What/why was that?
If you're doing it now of course it still applies, what do you find most difficult about the subject?

Think about your personal experience

I'll be happy to hear your answers, thanks in advance

Luis

[SapereAude1490]

Lacking knowledge in math and physics, semantics...

For example; how come the closer the electron is to the core, the lower it's energy state and, at the same time, you need more energy to kick it out (ionize it). Stuff like that.

[fledarmus]

The biggest problem I had was just understanding the physical meaning behind the math. Having grown up with the planetary theory of electrons, it was very difficult to wrap my head around the idea of an orbital being a probability field. Especially since I had no idea what a probability field was either.

[Jorriss]

1) The majority of the class had difficulty with the math. Most people did not retain the the concept of taylor expansions so naturally expanding in terms of some arbitrary basis in quantum was even more difficult. People also lacked linear algebra and differential equation knowledge.

2) My biggest problem was the concepts. Wave-particle duality is tricky and I still don't think I get it properly.

[curiouscat]

The biggest problem I had was just understanding the physical meaning behind the math.

This.

Also: bra-ket notation; operator algebra; ladder operators; spin.

In most other classes either the math is new or the application but rarely both. It did't help that in the Quantum class we were trying to learn a new field with entirely new tools that we'd never had a chance to use much before.

Mostly the fact that it seemed closest to magic I ever got to in a Science class.

[vex]

Mostly the fact that it seemed closest to magic I ever got to in a Science class.

Totally true.

I took a grad-level quantum class last year, and the professor took two weeks to hammer out linear algebra and some other useful math concepts (we were working in the Heisenberg formulation so we didn't really touch differential equations). I don't know how pressed for time you are, but if you were to throw in a math chapter or two, your students would be eternally grateful. Maybe.

[Enthalpy]

This site can be helpful:
http://winter.group.shef.ac.uk/orbitron/

My background was full of waves (EM, acoustic, Fourier, antennas...) and this helped a lot.

Perhaps the biggest obstacle were all the stupid comparisons by the Press, with all the "surfer and wave at the same time"...
For orbitals you can say "the electron is a wave" and that's enough.

O yes, over-simplified models made things more complicated to me: plane waves without any spatial nor temporal bounds, 2D or 1D mathematical solutions...

What about beginning with the atom? It illustrates nicely the non-local particle, the equivalence between basis with propagating and standing waves (on p orbitals, doughnut or peacock shaped), the uncertainty on the XYZ spin (with p orbitals), interferences by superposition of states and link with E-field polarization and photon emission or absorption, and stability of stationary states, entanglement of photons... I feel the atom very concrete, and a door to more general ideas.

Difficulties... I only I had just one biggest! Particle spin, exclusion principle. Also: why should a photon interact sometimes with one single electron and sometimes (diffraction by crystals) with many ones. And of course, things like EPR, when mental representations by just a deterministic wave able to behave as an uncertain particle isn't enough. As well, multi-photon absorption and frequency doublers, which I feel fit the wave models only without the usual particle rhethoric.

[juanrga]

Hi everyone,

I'll soon be teaching quantum chemistry privately, and I'd like to ask you:
When you took your first course about quantum mechanics: Did you find something about the subject particularly difficult? What/why was that?
If you're doing it now of course it still applies, what do you find most difficult about the subject?

Think about your personal experience

I'll be happy to hear your answers, thanks in advance

Luis

Probably the biggest difficulty is the lack of an underlying physical picture behind the maths. E.g., you are explained what is the equation of motion, but then no intuitive/visual model of motion is given and when you ask questions such as «how does the electron move from the emitter to the detector in a double-slit experiment?» You receive a simple «quantum mechanics does not answer such questions». In the end you learn to solve some equations and little more.

Another source of difficulty is that most introductory treatises on quantum mechanics present the subject using old ideas such as wave-particle duality and similar ones. I would recommend Ballentine textbook, Quantum Mechanics: A modern development, which criticizes and avoids many of those old ideas. See as well Klein's site.

[Jorriss]

Another source of difficulty is that most introductory treatises on quantum mechanics present the subject using old ideas such as wave-particle duality and similar ones. I would recommend Ballentine textbook, Quantum Mechanics: A modern development, which criticizes and avoids many of those old ideas. See as well Klein's site.

Ballentine is a pretty advanced book. It's probably not a good first exposure.

[juanrga]

Another source of difficulty is that most introductory treatises on quantum mechanics present the subject using old ideas such as wave-particle duality and similar ones. I would recommend Ballentine textbook, Quantum Mechanics: A modern development, which criticizes and avoids many of those old ideas. See as well Klein's site.

Ballentine is a pretty advanced book. It's probably not a good first exposure.

Maybe Ballentine textbook would be used only by the instructor before giving a quantum chemistry course to its audience; whereas, the Klein website must be more accessible to that audience.

[Jorriss]

Another source of difficulty is that most introductory treatises on quantum mechanics present the subject using old ideas such as wave-particle duality and similar ones. I would recommend Ballentine textbook, Quantum Mechanics: A modern development, which criticizes and avoids many of those old ideas. See as well Klein's site.

Ballentine is a pretty advanced book. It's probably not a good first exposure.

Maybe Ballentine textbook would be used only by the instructor before giving a quantum chemistry course to its audience;

That's a good idea. Ballentine's book is really good - it's the first book I saw that really explained state preparation well. Another good text, which some more prepared students might be able to handle is Zettili.

[saito200]

Awesome answers, I could already extract some meaningful ideas for my teaching.

I myself have often problems connecting the maths to any physical meaning and that's the most difficult part for me. For instance, I could clearly see only recently the relation of Fourier theory and eigenstates of x constructed as an infinite sum of eigenstates of p.

I'd love more suggestions about online resources. I'll let you know how things work

Thank you all for the help
Luis