Recent content by borgwal

1. Commutator and hermitian operator problem

What this example also shows is that in *finite* dimensions you cannot have two hermitian operators A and B satisfying [A,B]=cI
2. Quantum Energy Levels

For j=1/2 there are two states: m=+/- 1/2, and for j=3/2 there are 4 different m-states. The "weak" Zeeman effect just refers to a situation where the energy shift due to the magnetic field is small and can be treated with perturbation theory: the unperturbed Hamiltonian has split the l=1 level...
3. Quantum Energy Levels

It's because the interaction that splits the energies of the state is the spin-orbit coupling, proportional to \vec{L}\cdot\vec{S}, which can be rewritten as being proportional to the difference \vec{J}^2-\vec{L}^2-\vec{S}^2, which is dependent only on the quantum numbers j and l (s=1/2 in...
4. Uncertainty Principle

Once you have answered part (b), you will see that the relation that you're supposed to prove in part (a) cannot be quite correct!
5. Angular Acceleration (I don't see HOW I can be wrong?)

Yes, 3g/2L it is.
6. Proving a matrix is unitary

You clearly did not state the full problem so I have to keep guessing: were you supposed to diagonalize the Hamiltonian and find U such that [tex] H=\sum_k E(k) b^+_kb_k [/itex]?
7. Proving a matrix is unitary

If the b's are fermionic annihilation operators, then that *means* they satisfy the anticommutation relations that, as you figured out, are equivalent to U being unitary. Done.
8. Proving a matrix is unitary

You need more information to prove any of those relations. You must have been given some info about what the b's are supposed to be, for instance. I assumed that you had been told that the b's are fermionic annihilation operators.
9. Electrostatics charge density

First, is the vector \vec{r} in E meant to be the *unit* vector in the r-direction, or not?
10. Trapped Electrons

It's because a photon carries angular momentum, but in 1-D the concept of angular momentum is not defined.
11. Print ViewSimultaneous Measurements of Position and Velocity

So far so good! Now the other thing you have been given is that delta v_x is 1% of v_x.
12. Normalizing Wave Function of A Ring

You just took the square of the wavefunction, instead of the absolute value squared.

Yeah.
14. Average net force

There are (at least) two sorts of average you can take: If you want to calculate a force averaged over *distance*, you can use the change in kinetic energy, divided by distance: Work =\delta E=F_average * d If you want to calculate an average over *time*, then that would be given by the change...
15. Proving a matrix is unitary

No, you have to prove U is unitary. Edit: you already seem to know that U being unitary is equivalent to the b's satisfying the same anticommutation relations as the c's. But that's all there is to it....