Recent content by TheBaker

Right, I think I've got it. So since we know that the coefficient of m=0 is a factor of \sqrt{2} larger than m=±1, we find that... P(m=0) = 0.5 P(m=1) = 0.25 P(m=-1) = 0.25 Hopefully, that's right. Thanks for everyone's help, I think I understand it all slightly better now (cue everyone...

Through a combination of the textbook and lecture notes, I get the constants to be: c_1^0 = \sqrt{\frac{6}{8 \pi}} and c_1^{\pm 1} = \pm \sqrt{\frac{3}{8 \pi}} However, the sum of the square of these doesn't equal 1 - am I supposed to include the Y function when squaring to find the probability?

Because the functions that form the systems wave function are the three spherical harmonics of l=1.

Thanks, so the eigenvalue of L^2 is 2 \hbar^2, which must presumably have a probability of 1 as it's the only eigenvalue. The eigenvalues of L_z are -\hbar, 0, \hbar, but how do I figure out their probabilities? Sorry if this is a really stupid/easy question - as you can probably tell, QM...

Homework Statement The angular part of a system’s wavefunction is <\theta, \phi | \psi>\propto (\sqrt{2}\cos\theta + \sin{\theta}e^{−i\psi} - \sin{\theta}e^{i\psi} ). What are the possible results of measurement of (a) L^2 , and (b) L_z , and their probabilities? What is the...

It's not (2pi)^2 on the bottom, it's just 2pi. Plugging in the numbers with the modified formula gives the correct value.

I'm doing some research into time travel for a presentation I have to give in a month or so, and I'm currently looking at the compatibility of Time Travel and the Laws of Conservation. Sending an object back in time would increase the mass - and hence the energy - in the Universe at this...

The sin solution isn't valid because this well has even parity (i.e. it's symmetric). How do I find A? Presumably I need to use the initial condition of Psi, but I found when doing that that A is x dependent, when it should be a constant.

The easiest way I find to solve problems like this is to solve the problem twice - once where the contents of the modulus are positive anyway, and once when they're negative (in which case you need to put an extra minus sign in front of them).

Homework Statement A particle is trapped in an infinite potential well, with the infinite walls at ±a. At time t=0, the wavefunction of the particle is \psi = \frac{1}{\sqrt{2a}} between -a and a, and 0 otherwise. Find the probability that the Energy of the particle is \frac{9...

Sorry, that should indeed be +3

Homework Statement The density of ice is 0·92×103 kg m−3 and its latent heat of fusion is 3·3×105 J kg−1. Estimate the melting temperature of the ice at the bottom of a glacier which is 100m deep. Homework Equations L = Tc(S2 - S1) The Attempt at a Solution (S2 - S1) = 1208.8 I then...

Ah, gotcha. Thanks.

This is probably just me being a bit of an idiot (I'm going to blame exam stress), but why do the following ways of calculating the volume and lateral area of cones produce different results? I'll use the following equation of a cone to demonstrate: x^2 + y^2 = \frac{9}{4}z^2 (Valid for 0...

Ah, I've got it now (I ended up using the integral form of Gauss's law, but it boils down to the same thing). Thanks for your help.