QM before Lagrange/Hamiltonian mechanics?

[ice109]

Can someone please explain to me the sense in teaching quantum mechanics before lagrangian and hamiltonian mechanics?

While in undergrad I took a course in intermediate mechanics which was from the first couple of chapters of marion and thornton - like 1-4 or something like that. Then I took qm for an entire semester before taking advanced dynamics where we briefly discussed lagrangian and hamiltonian formalisms. Now this is not because I chose to do this - the classes are setup as such. QM 1 is offered fall and then QM2 is offered spring concurrently with Advanced dynamics.

Now I'm taking the graduate QM class and the graduate students in my class are just now, this late in the semester, being exposed to the beginnings of the lagrangian formalism in their mechanics class. I sat in the other day and they were doing the pendulum problem.

I wager this is not unique to my school. The entire time I've been learning QM I'm constantly questioning things whose motivations come hamiltonian and lagrangian mechanics. I bet most other students are as well.

Anyone have some opinions?

 

[Monocles]

I guess it depends on your school. My intermediate mechanics class used Marion and Thornton as well. I don't remember what chapters we covered specifically, but we definitely did a good amount on Lagrangian and Hamiltonian mechanics. I haven't taken the advanced mechanics yet, so I don't know what is covered in there, but I guess your professor avoided it for some reason.

 

[Mororvia]

I learned L/H mechanics in my first undergrad mechanics course, reviewed again in my 2nd, and did it again while in graduate school. Are you sure the graduate students are just learning it for the first time or are you assuming ?

Either way, I don't think it matters too much if you learn QM before L/H mechanics. Maybe I missed something fundamental but I didn't really see too much of a connection besides some of the terminology (Hamiltonians).

 

[ice109]

I learned L/H mechanics in my first undergrad mechanics course, reviewed again in my 2nd, and did it again while in graduate school. Are you sure the graduate students are just learning it for the first time or are you assuming ?

of course they probably were exposed to it at their undergrad institutions but at what level i don't know.

Either way, I don't think it matters too much if you learn QM before L/H mechanics. Maybe I missed something fundamental but I didn't really see too much of a connection besides some of the terminology (Hamiltonians).

is that a joke? you think the hamiltonian of a quantum system is not the same thing as the hamiltonian of a classical system?

though you're lucky to have seen lagrangian/hamiltonian mechanics as often as you did.

monocles: it's not that my professor avoided it, it's that we didn't progrress that far into the book.

 

[arunma]

I actually only had a single semester of advanced mechanics in undergrad, in which I spent two or three weeks on Lagrangian/Hamiltonian mechanics. All the other L/H stuff I learned was either from studying for the qualifier, or taking field theory. It's never been much of a hindrance to me. Except that for the longest time I actally believed that a Hamiltonian was (in general) just the total energy in a system.

 

[Vanadium 50]

Can someone please explain to me the sense in teaching quantum mechanics before lagrangian and hamiltonian mechanics?

Because it requires less mathematics. Ideally, you wouldn't take E&M, Classical Mechanics or Quantum Mechanics until you knew the other two, but since that's impossible, something has to go first, and most schools have decided that QM is the best choice.

 

[ice109]

Because it requires less mathematics. Ideally, you wouldn't take E&M, Classical Mechanics or Quantum Mechanics until you knew the other two, but since that's impossible, something has to go first, and most schools have decided that QM is the best choice.

how is that even true? how is functional analysis any less daunting than phase space analysis or something like that.

ideally one learns all of cm then all of em then all of qm

 

[Pengwuino]

is that a joke? you think the hamiltonian of a quantum system is not the same thing as the hamiltonian of a classical system?

I'm sure that's not what he meant. For example, I gather many universities have a sort of upper division modern physics course that goes over high energy physics, special relativity, quantum mechanics, and the sorts in more detail then your undergraduate courses but still, not in too much detail. It isn't silly to say that it's not very important to have not had your full classical mechanics and electrodynamics courses before that because the modern physics course isn't there to go through the detailed formalism.

When I took my grad QM, I hadn't taken my grad classical and honestly, it didn't matter. You can't expect the QM class to go through everything you need to know from CM; it needs a jumping off point that simply says "this is from what we know from CM". What you're left with is various holes and understandings that aren't perfectly formalized, but the fact of the matter is that you WILL learn it and unless you have a horrible time relating classes, you'll fill in those gaps soon enough.

 

[Vanadium 50]

First year QM requires a little differential equations and a goodly bit of linear algebra. Classical mechanics requires maybe a little less linear (although my undergraduate class had us solving lots of coupled oscillator problems, so I had rather a lot) and a lot more in the way of DE's, as well as calculus of variations. E&M doesn't have much in the way of linear or calculus of variations, but there's an avalanche of analysis. For these reasons, it's common to start the upper division courses with quantum.

There's another reason - often there are two courses in QM and only one in Classical, E&M and Stat Mech. Since there's more material, it makes sense to start sooner.

 

[Mororvia]

is that a joke? you think the hamiltonian of a quantum system is not the same thing as the hamiltonian of a classical system?

I'm sure that's not what he meant.

Right, it wasn't a joke and also not what I meant. Maybe a better way for me to explain it is to say I learned Hamiltonian mechanics in my classical courses and I learned about Hamiltonians in my QM courses. Never while doing problems in either course did I say to myself, "Hey, I know how to do this in classical mechanics so I understand this in quantum mechanics!"

So yes, it is the same thing but knowing it from classical never helped me in quantum. To answer your original question, yes it makes sense (to me) teaching quantum mechanics before lagrangian and hamiltonian mechanics because knowing about it in one never helped me with the other.

 

[dx]

Only in quite advanced aspects of QM does one need a real understanding of hamiltonain mechanics, canonical transformation etc. It is certainly not a prerequisite for introductory quantum mechanics courses.

 

[Astronuc]

Can someone please explain to me the sense in teaching quantum mechanics before lagrangian and hamiltonian mechanics?

I seem to remember that QM was taught concurrently with lagrangian and hamiltonian mechanics. There was an introductory course to modern physics including QM up through Schrödinger's equation, which was a prelude to the first major QM course. One was also expected to have a course in partial differential equations.

 

[Pinu7]

The mathematical prerequisites in physics is messed up.For classical mechanics, you need to know differential geometry, lie groups, etc to just get by.

For (introductory )Quantum Mechanics, you just need to know a bit of linear algebra.

Of course, Quantum Mechanics is not as cool if you do not know the Poisson bracket-commuter relation.

A quick overview of CM before a QM mechanics class( just up to PB) is fine. You do not need "Hamiltonian Mechanics on Slymplectic spaces" for Quantum Theory.

 

[George Jones]

how is that even true? how is functional analysis any less daunting than phase space analysis or something like that.

Usually, not much of even a physicist's version of functional analysis comes into play in an introductory quantum physics course, and too much time spent on rigourous functional analysis can lead to "rigour mortis" in an advanced quantum theory course. Don't get me wrong, I do think that some physicists should learn some functional analysis. But I don't think it needs to be universal.

In third year, I was required to take took two semesters of classical mechanics (Goldstein) and two semesters of introductory quantum theory. In fourth year, I was required to take two more semesters of quantum theory. I also took a course in functional analysis, but I was not required to do so.