Recent content by umagongdi

thanks

I asked the proffesor and he said the same, that the answer was just for the z-axis, he didn't explain. Why is this for the z-axis? Is the total spin just the sum of all the spins? But we don't know the nuclear spin etc?

Oh i think i get it now thanks. You can just separate the wave function like this? Y0(x,y,z)=e-x2/2+e-y2/2+e-z2/2

Homework Statement A helium atom had two electrons in the first shell (1s). Explain, withour detailed derivation, what the value of the total spin quantum number is. Homework Equations ? The Attempt at a Solution Since the 2 electrons are in the first (1s) shell they must have...

Homework Statement a.) The motion of a particle in the 3-dimensional space is described by the Hamiltonian H = Hx+Hy+Hz, where Hx=1/2*(px2+x2), Hy=1/2*(py2+y2), Hz=1/2*(pz2+z2) Check that the standard angular momentum operators Lx, is a constant of motion. b.) By knowing that the...

Sorry if this qs been asked before, i couldn't find one similar.

In this case is the eigenfunction HΨ=EΨ or eigenstate, what is the difference, are they the same? I am a bit confused is the whole equation HΨ=EΨ called a eigenfunction or a specific part of it? I think i finally understood how to do it, i used the ladder operator method. I obtained this part...

Can we look at HΨ=?Ψ We can rearrange and solve for Ψ?

lol that's awsome that we went/go to the same uni, what do you do now Masters/PhD here? As for the question, i don't understand how completing the square will help us find the eigenvalues. Looking at (1/2)mω2X2+ FX2 We can factorise the (1/2)mω2X2 (1/2)mω2X2(X2+FX/(1/2)mω2X2)...

Homework Statement Consider the Hamiltonian \hat{}H = \hat{}p2/2m + (1/2)mω2\hat{}x2 + F\hat{}x where F is a constant. Find the possible eigenvalues for H. Can you give a physical interpretation for this Hamiltonian? Homework Equations The Attempt at a Solution I don't think...

or you can just add them together [A,B]+[A,B] = Re(λ)+iIm(λ)-Re(λ)+iIm(λ) 2[A,B] = 2iIm(λ) [A,B] = iIm(λ) Is it better to write this?

Oh i get it now :) First you need to adjoint to obtain an equation, which you can compare to the original. LHS [A,B]+=(AB-BA)+=BA-AB=[B,A]=-[A,B] RHS λ+= Re(λ)-iIm(λ) [A,B]= -Re(λ)+iIm(λ) comparing this to the original [A,B]= Re(λ)+iIm(λ) Therefore Re(λ)=-Re(λ) and...

[a,b]+=(ab-ba)+=ba-ab=[b,a]?

You need to use the fact that A and B are Hermitian. A common tactic is to take the adjoint of both sides of an equation. Try that. We know that A is Hermitian if A=(A*)T. So maybe, [A,B]=Re(λ)+Im(λ) [A*,B*]T=(Re(λ)+Im(λ))*T =(Re(λ)-Im(λ))T...

Homework Statement Suppose that the commutator between two Hermitian operators â and \hat{}b is [â,\hat{}b]=λ, where λ is a complex number. Show that the real part of λ must vanish. Homework Equations Let A=â B=\hat{}b The Attempt at a Solution AΨ=aΨ BΨ=bΨ...