Do I Need Classical Mechanics to Understand Quantum Mechanics?

[zahero_2007]

Do I need Classical mechanics and waves in order to understand Quantum mechanics?

In order to learn quantum mechanics , do I need to know Classical mechanics and Waves or only linear algebra and calculus?

 

[cristo]

Yes, you should learn classical mechanics before tackling quantum mechanics.

 

[zahero_2007]

Thanks , cristo

 

[dextercioby]

Classical mechanics is mandatory in the Lagrange, Hamilton and Hamilton-Jacobi formalisms. And as much mathematics as possible, of course.

 

[Andy Resnick]

In order to learn quantum mechanics , do I need to know Classical mechanics and Waves or only linear algebra and calculus?

I'm going to play devil's advocate and say no.

Obviously, the mathematics developed for classical mechanics is used in quantum mechanics, and quantum mechanics makes use of things like harmonic oscillators that have a clear interpretation in classical mechanics. But, I think quantum mechanics can be taught without knowing anything about inclined planes, free body diagrams, forces, etc. It should be possible to teach Quantum mechanics first, with the reduction to classical mechanics introduced later.

 

[jtbell]

You do need to be familiar with the concepts of energy (both kinetic and potential) and momentum, for basic one-dimensional QM. Add angular momentum when you move up to 3-D systems (e.g. the hydrogen atom).

 

[twofish-quant]

But, I think quantum mechanics can be taught without knowing anything about inclined planes, free body diagrams, forces, etc. It should be possible to teach Quantum mechanics first, with the reduction to classical mechanics introduced later.

It's possible but in order to deal with quantum mechanics you need to have good physics problem solving skills, and the standard way of getting those skills is through classical mechanics and waves. The important thing about classical mechanics is that you can physically touch blocks and bricks in a way that is more difficult to do with quantum mechanics.

You standard intro physics class really is "introduction to physical problem solving methods". The fact that it happens to be classical mechanics is something of a historical accident.

 

[Andy Resnick]

You do need to be familiar with the concepts of energy (both kinetic and potential) and momentum, for basic one-dimensional QM. Add angular momentum when you move up to 3-D systems (e.g. the hydrogen atom).

It's possible but in order to deal with quantum mechanics you need to have good physics problem solving skills, and the standard way of getting those skills is through classical mechanics and waves. The important thing about classical mechanics is that you can physically touch blocks and bricks in a way that is more difficult to do with quantum mechanics.

You standard intro physics class really is "introduction to physical problem solving methods". The fact that it happens to be classical mechanics is something of a historical accident.

I hear what you guys are saying, but that doesn't address my claim- all of those topics (and more) can be first introduced in a QM class.

Now, to be fair, for a non Physics major it probably doesn't make sense to 'skip' Newtonian mechanics.

From where I sit, any increase in the level of abstraction is more than compensated by getting rid of the continuous apologizing for results like tunneling, Shrodinger's cat, and nonlocality.

The standard curriculum needs an overhaul. QM is nearly 100 years old. Isn't it time to stop calling it 'modern'?

 

[petergreat]

I'm going to play devil's advocate and say no.

Obviously, the mathematics developed for classical mechanics is used in quantum mechanics, and quantum mechanics makes use of things like harmonic oscillators that have a clear interpretation in classical mechanics. But, I think quantum mechanics can be taught without knowing anything about inclined planes, free body diagrams, forces, etc. It should be possible to teach Quantum mechanics first, with the reduction to classical mechanics introduced later.

The most logical order of doing things is as follows. 1. Teach all the math needed. 2. Teach QM. 3. Derive classical mechanics as a macroscopic limit. 4. Teach classical mechanics.

The advantage is that you won't get student complaining that quantum mechanics is so weird since it's probabilistic. If QM is what they're taught in their first course in physics, they aren't going to complain. Instead, after you derive classical mechanics as a macroscopic limit, students will be puzzled, "Wow how can you possibly get a theory in which there's no probability? That's so counter-intuitive!" Another advantage is that by the time they learn classical mechanics, they're already familiar with Hamiltonian and Lagrangian formalism, and Newton's laws just need to be derived from one of them.

 

[twofish-quant]

The standard curriculum needs an overhaul. QM is nearly 100 years old. Isn't it time to stop calling it 'modern'?

QM only entered the physics curriculum in the mid-1960's. Something that is interesting is to read on *how* the standard physics curriculum came into being. What happened was that in the 1960's, people thought that the US and the USSR were in a life and death science struggle, so a lot of what developed was trying to teach large numbers of people quickly. Large lecture halls have taken a beating but the reason for that to get created was it's a very cheap and efficient when you have large numbers of students and few teachers.

Also, one has to ask what the "purpose" of teaching QM is. When I learn QM, the class didn't go over non-locality or "weird stuff." The main point of the class was to teach engineers to use QM to build better machines, and so weird stuff like EPR wasn't covered in the class.

 

[twofish-quant]

The most logical order of doing things is as follows. 1. Teach all the math needed. 2. Teach QM. 3. Derive classical mechanics as a macroscopic limit. 4. Teach classical mechanics.

There are lots of ways of doing it. However, one problem with teaching things in this way is that you run the risk that it becomes a math game rather than connecting math with observations. Something that's pretty easy to do with classical mechanics is that you can drop and apple and see how the apple dropping matches your equations (and finding out that it never matches exactly.)

 

[Andy Resnick]

The most logical order of doing things is as follows. 1. Teach all the math needed. 2. Teach QM. 3. Derive classical mechanics as a macroscopic limit. 4. Teach classical mechanics.

My quibble with this is that math doesn't have to be taught prior to anything else- we are talking about a *physics* curriculum, not a *math* curriculum. Physical concepts can be introduced alongside mathematical machinery.

 

[Andy Resnick]

QM only entered the physics curriculum in the mid-1960's.

I'm not sure that's true (although it may be if we talking about undergraduate education), but fine- the undergrad curriculum has existed unchanged for 50 years. Again, that's not modern.

 

[Einstein Mcfly]

Sorry to dig up such an old thread, but I found this discussion really interesting. I've long thought that the way things are taught is a relic of some earlier time and (at least with chemistry) you end up teaching a lot of things to young undergrads that are dumbed down or made slick for the purposes of comprehension that they will have to basically unlearn later on in their undergraduate (or certainly graduate) career. Things like the Bohr atom that does nothing but cater to their classical prejudices and give exactly the wrong idea of how to best picture an electron are kept around only to make life harder for the poor graduate TAs that end up spending all the time telling them that what what they "know" is just a silly cartoon.

Anyway, I'm interested in two things: 1) How to best avoid teaching things in this way in a era when lessons are constrained by standardized tests that expect students to be ready for plug and chug type questions involving semi to totally incorrect concepts and 2) what's a good textbook (advance undergrad or graduate level is fine) that discusses classical mechanics as the macroscopic limit of QM?

Thanks for any help.

 

[epenguin]

If the students of medicine and biology, who have to learn biochemistry as a necessary basis for that, and then have to learn chemistry as the basis for biochemistry and have to learn quantum mechanics as basis for chemistry also have to learn a lot of classical mechanics before qm (and then why not right down the food chain to the logical foundations of mathematics, in theory underlying the rest?) they will never get where they need to. So something that seems to its professors a necessary basis of something else has to be, and in practice is, compromised (or dumbed-down).

Contrasting with the insistence 'you have to do this before you can do that' is the didactic principle of 'run before you can walk'. Then when something is needed there will be more motivation to study it and more efficiency. While stuff justified by 'you will need it' can be poorly learned or forgotten. Do you univ teachers not meet students who officially have done the math at school where they were told it will be useful somehow someday but have forgotten it or are unable to use or apply it?

There are practical problems on the other side, you cannot always be going back to doing basics for the first time at the moment you need to apply them but I think a corrective to the rigid this-before-that which may seem the logical order is necessary.

 

[chill_factor]

For what its worth:

i learned what a Hamiltonian was for the first time in a quantum chemistry class.

Of course, you have to pass basic physics which includes classical mechanics and waves. you have to know what those things are, but in my experience i didn't need to be able to calculate the orbital mechanics of Voyager 2 to understand atoms and molecules.

 

[Jorriss]

Some classical mechanics help. You should know somewhat what angular momentum is for example. But its not like you need a full upper division sequence of classical mechanics before quantum.

 

[Robert1986]

As a math guy, allow me to give my two cents. First of all, it makes no sense to teach QM to students who are not physics majors (that is, of course, unless they WANT to take it, then they can just sign up.) It is far more sensible to teach us uninitiated folks the classical stuff, since, as someone pointed out, we can touch blocks in a way that is difficult to do with atoms. My two semesters of Physics gave me a pretty good understanding of classical stuff. That being said, I plan to take QM as a grad student.

Secondly, to me, teaching QM then Classical stuff is a bit like teaching Analysis and then Calculus. In principle, it can be done, but analysis requires a certain amount of mathematical maturity just as QM requires a certain amount of "physical maturity."

 

[Jorriss]

Secondly, to me, teaching QM then Classical stuff is a bit like teaching Analysis and then Calculus. In principle, it can be done, but analysis requires a certain amount of mathematical maturity just as QM requires a certain amount of "physical maturity."

Imo, this is a very well put comparison.

 

[bpatrick]

I don't see anything wrong with the current system, but I also think there are many ways to go about learning that can be just as effective. I was fine with learning loads of math and chemistry concurrently, then simply jumping into "upper level undergraduate" physics.

I had multivariable calc, statistics, linear algebra, ODEs, PDEs, and combinatorics/graph theory ... then took quantum mechanics and statistical mechanics in the same semester without having taken any physics courses other than a high school algebra physics overview.

I didn't have much trouble learning physics that way. I guess there were a few things that were harder for me to tackle since it was the first time I was seeing much of the material. My chemistry background helped out a bit for that, but not as much as a physics sequence would have. At least I had the necessary math preparation, there were some guys in the course who struggled due to issues they were having with their mathematics preparation.

 

[Mike H]

It is far more sensible to teach us uninitiated folks the classical stuff, since, as someone pointed out, we can touch blocks in a way that is difficult to do with atoms.

Perhaps this is an argument for more thoughtfully devised physics/chemistry laboratory experiences & courses for students.

One of the most memorable scientific experiences I had an as an undergraduate was doing ESR studies of organic dyes bound to proteins (admittedly, this was in the lab where I did my undergraduate research and not in a standard laboratory course), and being able to predict (qualitatively) spectral changes using a simple "particle in a box" model. When it actually panned out, I was rather excited.

 

[Einstein Mcfly]

Sorry to dig up such an old thread, but I found this discussion really interesting. I've long thought that the way things are taught is a relic of some earlier time and (at least with chemistry) you end up teaching a lot of things to young undergrads that are dumbed down or made slick for the purposes of comprehension that they will have to basically unlearn later on in their undergraduate (or certainly graduate) career. Things like the Bohr atom that does nothing but cater to their classical prejudices and give exactly the wrong idea of how to best picture an electron are kept around only to make life harder for the poor graduate TAs that end up spending all the time telling them that what what they "know" is just a silly cartoon.

Anyway, I'm interested in two things: 1) How to best avoid teaching things in this way in a era when lessons are constrained by standardized tests that expect students to be ready for plug and chug type questions involving semi to totally incorrect concepts and 2) what's a good textbook (advance undergrad or graduate level is fine) that discusses classical mechanics as the macroscopic limit of QM?

Thanks for any help.

Anyone?

 

[homeomorphic]

Quantum mechanics seems kind of "out of left field" to me without knowing something about Hamiltonian mechanics and waves. Schrödinger's equation has a Hamiltonian operator in it that comes from quantizing a classical Hamiltonian. So, yes, I think you have to know classical mechanics to understand quantum mechanics. Otherwise, you'll be missing a lot of motivation, I think.