Hi
Most of my work in the past has been on 1D independent particle systems where I use matrix diagonalisation to solve the time-independent Schrodinger equation.
How do I go about this for 2D? Or, more accurately, for a two-body wf in 1D? It strikes me as straightforward to construct a...
Is there something wrong with my wording here? Please tell me if there is and I will amend the question. I could do with sussing this in the next week. Cheers... EHI
Hi there. Long time no see. I hope you're all well.
Homework Statement
An infinite 1D system has electron plane waves occupying states 0 <= E <= E_F. At time t=0, a potential step is introduced such that V=0 for x<0 and V=V' for x>0. What is the electron density when the system reaches...
Apologies, that should have been 'adiabatic expansion' not 'free expansion'. Turned out my solution was correct: I had stupidly used the net heat instead of the heat in when evaluating the efficiency though, so I thought, as I had expected, my method was wrong. All's well that ends well...
[SOLVED] Work and heat transferred in ideal engine
Homework Statement
System is ideal engine containing one mole of ideal gas.
System in initial state P1, V1, T1.
System undergoes free expansion along adiabat to P2, V2, T2.
System undergoes isothermal compression to P3, V3, T3.
System...
Same thing. If something is generally true, it is always true.
A ha! Penny's dropped. dW = P dV is NOT true while the system is out of equilibrium (i.e. while the shock wave is propogating) but is true once the system is back to equilibrium. Yeah, that's me not spotting the red-herring in...
I was talking about your statement of it, not the generally true law, in the same way that:
Clearly one cannot say that since a law is a law this is generally true - it is a special case, but is still referred to in this and other sources as a statement of the 1st law for reversible...
Hi Andrew, thanks for the comments.
I'm not sure that was the required answer as we then went on to show how U was independent of P and V for an ideal gas (and not for a real gas of high-ish density). I think the issue here was perhaps my use of the word 'derive' rather than 'state...
Turned out, just in case anyone was following this thread (from my course, for instance) that the aim was to derive that expression using a path in PV space comprising of first a change from the initial isotherm to the final isotherm at constant volume (so no work done) and second a move down...
Hi
Yeah, that's my latexing again. If you click on it you'll see I did put a \frac in there but to no avail. I don't know why they come out like that but I just don't spend enough time on here to get to grips with the grammar.
Cheers. Yes, that does seem overcomplicated, to the point where...
Hi nrqed
Yes, Lz is diagonal. In fact, I'll struggle with LaTex and tell you the matrices:
L_{x} = \frac{\hbar}{\sqrt{2}} \left(\begin{array}{ccc}0&1&0\\1&0&1\\0&1&0\end{array}\right)
L_{y} = \frac{\hbar}{\sqrt{2}} \left(\begin{array}{ccc}0&i&0\\-i&0&i\\0&-i&0\end{array}\right)...
Oops. Accidentally hit the 'report' button instead of 'quote'. That was close. Somebody somewhere would be asking 'How exactly is this offensive...?'
Cheers Andrew for that stroll down memory lane. Haven't seen that equation for a while. It hasn't been brought up again in this or any...
Homework Statement
A fixed quantity of gas is originally at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of 50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat...
Hi
First off, those LaTex codes didn't quite come out the way I intended. Second, like I said I had no problem finding the eigenvalues of the matrix operators. The problem is in verifying them. I get the same eigenvalues for each matrix, i.e. mh, with the three possible values of m for l=1...
Hi
Homework Statement
We're given the operators Lx, Ly and Lz in matrix form and asked to show that they have the correct eigenvalues for l=1. Obviously no problem determining the values and Lz comes out right, however we've never actually seen the e.v.s for Lx and Ly.
Homework...