Recent content by holden

Heh. I never would have known that. Thanks. I went back through (from the beginning) and calculated the wavefunctions for n=2,l=0 and n=1,l=0 (2s and 1s for He+, respectively).. but what do I do with those? I know I'm supposed to write the ground state of tritium as a superposition of...

Hm.. There's no section about that in my QM book, and we haven't mentioned any of the terms you used in class. We've discussed a little bit about hydrogen atoms.. I think I'm supposed to use perturbation theory to find them.. but it's hard when I have no examples or any instruction about it =/

Really confused by this one. Homework Statement I'm given that a tritium atom, with one proton and two neutrons in the nucleus, decays by beta emission to a helium isotope with two protons and one neutron in the nucleus. During the decay, the atom changes from hydrogen to singly-ionized...

still not sure where i went wrong :(

I have in my notes that the x operator is defined as a_- - a_+.. that is wrong? I also have that a_-\psi_n = \sqrt{n\hbar\omega}\psi_{n-1} and a_+\psi_n = \sqrt{(n+1)\hbar\omega}\psi_{n+1}, so that's where the hbar's and omegas are coming from. Suppose that could be wrong too, though.. but...

Oh, OK. I was just leaving off the annihilation operator term. I already said that j = n+1 for the case involving the creation operator, and so the matrix element is -mg\sqrt{(n+1)\hbar\omega}. For the annihilation operator case, j must equal n-1 and you get -mg\sqrt{n\hbar\omega} for the...

Thanks for the response! I guess my question is that I don't know how to calculate the matrix elements.. I gave it a shot, though.. here's what I came up with: H_{jn} = <\psi_j^0|H^1\psi_n^0> = -mg<\psi_j^0|x\psi_n^0> = -mg<\psi_j^0|(a_-- a_+)\psi_n^0> =...

Homework Statement I'm given that a harmonic oscillator is in a uniform gravitational field so that the potential energy is given by: V(x)=\frac{1}{2}m\omega^2x^2 - mgx, where the second term can be treated as a perturbation. I need to show that the first order correction to the energy of a...

Sigh. Sorry. I feel like an idiot. OK. Thanks for spelling that out for me. So I did what you said and got a_-a_+\psi_0 = \psi_0. Applying the Hamiltonian and then using that, you get: [A(a_+a_-) + B(a_-a_+)]\psi_0 = E_0\psi_0 [(A(a_+a_-) + B]\psi_0 = E_0\psi_0 E_0\psi_0 = B\psi_0 So E0...

OK, maybe we didn't use that approach in my class because I can't find anything about it in my notes or text. So if we apply the hamiltonian to the ground state.. you get [A(a_+a_-) + B(a_-a_+)]\psi_0 = E_0. So since a_-\psi_0 = 0, you're just left with Ba_-(a_+\psi_0) = E_0.. which is...

OK, I see what you're saying. But since I don't know the lowering function explicitly here.. how can I calculate a_-\psi_0?

I'm not sure where the right half of that equation is coming from :(. I got the ground state energy by just saying a_-\psi_0 = 0 and [A(a_+a_-) + B(a_-a_+)]\psi_0 = E_0, and since a- operating on a state of energy E gives a state of energy (E - A - B), I reasoned that a- operating on E0 must...

Thanks guys. I think I did it in a convoluted way (before I saw your post, Hurkyl), but I ended up getting that a- operating on a state of energy E would give a state of energy E - A - B, and a+ operating on a state of energy E would give a state of energy E + A + B, which seems to make at...

Anybody have a clue on what I could do next? Even an inkling of an idea? Because I'm really lost. Do I need to provide more info? Thanks :)

Having a lot of trouble with this one. I'm given that the Hamiltonian of a certain particle can be expressed by H = A(a+a) + B(aa+), where A and B are constants and a+ and a are the raising and lowering operators, respectively. I'm supposed to find the energies of the stationary states for the...