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Help Me Understand Quantum (See: Witchcraft)
Fuzzy Cumulonimbus Cloud
Registered User regular
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I see a few of these threads every start of the semester but I can't find them, unfortunately.
I'm taking physical chemistry and we, (sigh), started with quantum mechanics.
My math is pretty good. I am not having a problem taking derivatives or integrating.
We are not expected to solve wavefunctions using differentials, so any second order solutions are already given to us. We are more expected to characterize the wavefunctions and use them to describe various characteristics of the atom.
What is frustrating is that he throws up massive amounts of gobbledy gook. I am really confused about the following things:
1) Hamiltonian Operator: he magics away large functions with this symbol, how do I expand it, or how do I know what it means?
2) Eigenfunctions: I cannot tell which part is the operator and which part is the function, but I do know how to tell if it is an eigenfunction, and if so, what its eigenvalue is.
3) Physical Systems: He kind of just assumes a bunch of background stuff that none of us have. Never have we been able to make our own systems or designate our own coordinate systems before. I have no idea what techniques or methods I should use to approach quantum questions.
Hope someone can help me.
I'm taking physical chemistry and we, (sigh), started with quantum mechanics.
My math is pretty good. I am not having a problem taking derivatives or integrating.
We are not expected to solve wavefunctions using differentials, so any second order solutions are already given to us. We are more expected to characterize the wavefunctions and use them to describe various characteristics of the atom.
What is frustrating is that he throws up massive amounts of gobbledy gook. I am really confused about the following things:
1) Hamiltonian Operator: he magics away large functions with this symbol, how do I expand it, or how do I know what it means?
2) Eigenfunctions: I cannot tell which part is the operator and which part is the function, but I do know how to tell if it is an eigenfunction, and if so, what its eigenvalue is.
3) Physical Systems: He kind of just assumes a bunch of background stuff that none of us have. Never have we been able to make our own systems or designate our own coordinate systems before. I have no idea what techniques or methods I should use to approach quantum questions.
Hope someone can help me.
Fuzzy Cumulonimbus Cloud on
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Quantum mechanics is physics and its very difficult to understand it properly without the required background in physics. Exactly what you need to know for the course, you should ask your professor.
To start, a hamiltonian is simply put, an operator. Its an H symbol that stands for a collection of functions. When you apply this operator to the wave equation, the eigenvalues are the allowed energy states.
The way eigenfunctions and eigenvalues work is actually much simpler than it is usually made out to be.
When you apply your operator (H) onto your function (psi) you get an eigenvalue (energy) * your function (psi).
Theres some physical reasoning behind why all solutions to the schrodinger are eigenstates, but thats not important.
For your purpose, generally H will stay the same as a 2nd derivative + a potential, but your wavefunctions will change depending on specifics of your electrons (1s 2p etc) and consequently when you apply the hamitonian to these functions, you'll get different eigenvalues (energies).
That would include things like fussing with coordinate systems and eigenfunctions. In fact, the "eigenvalue problem" is ultimately a question of matrix math. It might help to keep that in mind. Eigen isn't some fancy physics word, it's just German for "proper" or something. I can't really direct you to a good free linear algebra resource, but you can try searching or even looking at related math texts. Seeing it presented "dry" in its natural mathematical context may help.
As far as the Hamiltonian, in a simple way you might start off just considering it as shorthand for Schrodinger's equation. Do you know what the del operator is? It's probably something that comes up in vector calculus (what was calc 3 for me), http://en.wikipedia.org/wiki/Del_operator and basically it saves you effort, you may not have seen it yet. It's not a big deal. If you've dealt with gradients, you've dealt with it.
However, if you're not expected to actually do any differential equations (technically partial differential equations!) then it's hard to like...answer. I almost think things would be clearer if you saw a worked-out solution of Schrodinger's equation, but unfortunately my background is physics so of course I'll think that, and it's been too long since I've studied it to demonstrate it myself.
The easiest thing to do, as always, is to go grab your professor during his office hours. Many a grade has been salvaged
Edit: Oh goodness, look at me missing an opportunity to do this!! Google my name ^_^ I'm thinking it's been...four years since my QM class? How soon things start slipping...