Recent content by xago

Homework Statement According to wikipedia, one of the requirements of group is: For all a, b in G, the result of the operation, a • b, is also in G. So say we have 2 (2x2) matricies as elements of a group: \frac{0|1}{1|0} and \frac{w|0}{0|w^{2}} and the product \frac{0|1}{1|0} •...

Should I just assume a charge per unit length of Q on the cylinder, use gauss law to get the electric then derive that to get the potential which I simply add Vo to?

Homework Statement Construct a complex potential in the w-plane which corresponds to a charged metallic cylinder of unit radius having a potential Vo on its surface. The Attempt at a Solution I'm a bit confused on how to start deriving a complex potential for the cylinder. If I was given the...

Homework Statement http://img404.imageshack.us/img404/3952/contf.png The Attempt at a Solution Is there a set of rules or postulate that refer to which contour to use for specific integrals? I tried to use the residue theorem for the first integral but I didn't get the right answer

Homework Statement http://img4.imageshack.us/img4/224/32665300.png The Attempt at a Solution http://img684.imageshack.us/img684/2920/scan0003xo.jpg I've uploaded my work so far since its much faster than typing and I'm stuck on the last line trying to solve the integral. The first...

Would those be the case where only one spin is taken into account aka s=1/2, -1/2 which gives m_{j}= -3/2, -1/2, 1/2, 3/2 also, just to clarify, the only possible values for j are 1 and 2 right?

I just re-edited my 2nd post there, i confused m_{j} with m_{s}, but I know that for s=1 m_{s} is -1,0,1 which combined with m_{l} =-1,0,1 gives 9 states in total including the 3 given by s=0 right?

So if I understand correctly, j= l+s = 2 for l=1, s=1 which means that the possible values of m_{j} are -2,-1,0,1,2 which gives the possible states of: \begin{align*} &\vert s=1,\ m_s=-1;\ l=1,\ m_l=1\rangle \\ &\vert s=1,\ m_s=-1;\ l=1,\ m_l=0\rangle \\ &\vert s=1,\ m_s=-1;\ l=1,\...

Homework Statement There are 2 electrons, one with n=1, l=0 and the other with n=2, l=1. The question asks what is the dimensionality of total angular momentum space. Homework Equations (2j_{1}+1)(2j_{2}+1)The Attempt at a Solution I know for 2 electrons (spin 1/2 each) the possible values of...

Homework Statement I've obtained a recurrence relation of: a_{n+2} = \frac{(n-1)(n-2)-\frac{2k}{w_{o}^{2}}}{R^{2}(n+1)(n+2)}a_{n} from a Frobenius series solution problem and I've expanded it to give the series: f(r) = 1 + \frac{-\frac{2k}{w_{o}^{2}}}{6R^{2}}r^{2} +...

Homework Statement http://img18.imageshack.us/img18/8970/bose.png The Attempt at a Solution I'm on part b) where it asks which separation constation gives a harmonic time dependence. From part a) I deduced the equation \frac{d^{2}T}{dt^{2}}\frac{1}{T} = a constant. I'm choosing the constant...

Thats what I originally thought but I kept thinking i was missing something lol. So is it just A^2(6+1+4+9+16) = 1 A= 1/6

Homework Statement http://img857.imageshack.us/img857/2079/dirac.png Homework Equations H|ψ> = E|ψ> L^{2}|ψ> = l(l+1)\hbar^{2}|ψ> L_{z}|ψ> = m_{l}\hbar|ψ> The Attempt at a Solution I know this problem is very simple since I've seen a very similar problem a while ago but I've completed forgot...

The best I can do is 2k! which gives 2k(2k-2)(2k-4)...right? it works up k=3 to but it's missing the 2k+2 term and doesn't work for k=4 I know 2k! is expressed as 2^{k}k! but how is (2k+2)! expressed in such a way that I can calculate it? edit* oops, 2k! is right I believe. I miscalculated the...

Homework Statement I have a question with asks to solve a differential equation via power series and I've done everything up to finding the recurrence relation which is a_{n+2} = -\frac{a_{n}}{n+2} Given the initial conditions a_{o} = 1 and a_{1} = 0 I'm trying to simplify the series into a...