# Is it possible to take statistical mechanics without quantum mechanics?

## Main Question or Discussion Point

So I didn't start my physics major until my sophomore year which means I'm a year behind. Because of this I won't be able to take quantum mechanics until the first semester of my senior year which is also when statistical mechanics is offered. I'd really like to take statistical mechanics but quantum is listed as a prerequisite. How much quantum would I really need to take stat mech? Would it be enough to be taking quantum at the same time even if I hadn't had it previously? I don't really know enough about stat mech to know if it uses a lot of quantum mechanics or just uses some very basic stuff. What do you guys think about taking stat mech without quantum? I do plan on asking the professor who teaches the course eventually but I think I'll probably wait until the spring when it comes close to time to register for my senior year classes.

## Answers and Replies

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You just need to know a bit about the Pauli exclusion principle and maybe the infinite potential well. Of course knowing more never hurts but you don't need to.

jtbell
Mentor
In general, I'd be wary of bypassing prerequisite courses unless you've studied the material extensively yourself. Talk to the professor who's going to teach stat mech and see what he thinks. It may be like Klockan3 says and you won't actually need to know much QM, but I wouldn't gamble blindly about it. Different schools often take different approaches in what look like the same courses.

The way my school has it set up, we learn thermo and stat mech before quantum because of the scheduling of professors that teach it. It's not especially detrimental, but it's somewhat infuriating to work with equations that you haven't derived yet and seem to pop up like magic.

I'm taking quantum mechanics and statistical mechanics at the same time right now. It's fine - you don't need to know THAT much quantum mechanics. Just a handful of ideas that you could learn on your own.

Mute
Homework Helper
There are some important concepts from Quantum Mechanics that will come up in Stat Mech. You won't be sunk if you don't know them beforehand, but it may just seem like you're moving symbols around on a page with little understand why if you don't. Those concepts are:

-The Heisenberg uncertainty principle, $\Delta x \Delta p \geq \hbar/2$. This will come up when discussing writing down the partition function for an ideal gas or counting available states in a classical system, for example. One typically needs to coarse-grain the phase space into bins, and this provides the natual size of the bins.

-Discretization of energy levels: when writing down the partition function or counting states it's easier to work with discrete possibilities rather than continuous ones, so one typically deals with the discrete energy levels found in quantum mechanical systems, as there you don't need to worry about coarse-graining your phase space into discrete cells because it's already built in.

-Simple Harmonic Oscillator: You might calculate the partition function for the SHO both classically and quantum-mechanically.

-Bosons and Fermions and the Pauli Exclusion Principle: the statistical mechanics of bosons and fermions will naturally take into account some quantum mechanics and the exclusion principle.

You could probably take these concurrently and not be totally lost, and maybe even take stat mech without quantum at all, but it may be more conceptually difficult. You should probably ask your department for advice on the matter.