Recent content by bon

Thanks, sorry I wasn't clear. |k> and |i> are elements of the orthonormal basis. And I know that this means <k|i>=0 if k doesn't equal i. It's just that (as part of a larger calculation) I have arrived at the expression Ʃ(j)<k|j><j|i> (where |j> is also an element of the orthnormal basis)...

Homework Statement Suppose we have a system and that {|a>, |b>, ...} is a complete and orthonormal basis for the system Am i right in thinking Ʃ(j) <k|j><j|i> = <k|i> = 0 unless k=i? In other words, does the LHS expression equal the middle one because Ʃ(j) |j><j| is just the insertion...

Homework Statement Are the Lorentz transformations empirical laws? If so, are they empirically testable? Homework Equations The Attempt at a Solution I'm guessing they are. But how do you test the LT?

Homework Statement I'm trying to understand the preferred basis problem in the foundations of QM Ok so I read somewhere that in general any state can be decomposed in different ways. I don't quite see how this is meant to work Suppose 'up' / 'down' represent z component of ang mom...

Homework Statement Metric: ds^2 = -c^2 dt^2 + (t/t*) (dx^2 + dy^2 + dz^2) (I guess t* is a constant?) Is this universe matter dominant? Explain Homework Equations The Attempt at a Solution I guess you have to use the FRW equation? Assuming the usual FRW form, we set a^2...

Homework Statement Two photons travel along the x-axis of S, with a constant distance L between them. Find the distance between them as observed in S' (standard config - i.e. moving with speed v in x direction wrt S) How is this result connected to the Doppler effect? Homework...

Homework Statement In a given inertial frame S, two particles are shot out from a point in orthogonal directions with equal speeds v. At what rate does the distance between the particles increase in S? Homework Equations The Attempt at a Solution Ok so i want to write the...

It is correct yes! And no typo..this was on a past exam paper.

Homework Statement The Gibbs free energy of an elastic band satisfied dG = -SdT - LdF where F is the tension and L the string's length. At fixed temp the entropy is given by S = So - a(L-Lo)^2 + b(L-Lo)^2 Where Lo is the length of the elastic at zero tension and a and b are positive...

Homework Statement A system with two spins of magnitude 1/2 have spin operators S1 and S2 and total spin S = S1 + S2 B is a B-field in the z direction (0,0,B) The Hamiltonian for the system is given by H = m S1 . S2 + c B.S where m,c are constants. By writing the Hamiltonian in...

Homework Statement What magnetic flux density is required to produce a zeeman splitting of 0.05 /cm in the ground state of hydrogen? Homework Equations The Attempt at a Solution I\'ve worked out that delta E in the ground state is Ub B where Ub is the Bohr magneton. But how do...

Thank you!

Well that\'s basically what i said in my first post..but my question is: why do you have spherical symmetry when l=0. Surely if it is not orbiting, its at a given point - in which case the probability to find it in all directions shouldn't be the same!

Thanks but that doesn\'t help. I knew that already, as is clear from my post :) I\'m trying to understand it physically...

Homework Statement Give a physical explanation of why a spherically symmetric Ylm cannot describe the state of a system with non-zero angular momentum. Homework Equations The Attempt at a Solution I was thinking that if Ylm is spherically symmetric then the particle is equally...