Recent content by gasar8

I tried now in another way. By the definition of forms and change of coordinates (the Jacobi matrix) which is for p done also in Goodman. I write Lorentz matrix for boost in x direction, which is\Lambda_{\mu}^{\nu} = \begin{pmatrix} \gamma & \gamma \beta & 0 & 0\\ \gamma \beta & \gamma & 0 &...

Homework Statement I have an assignment to prove that specific intensity over frequency cubed is Lorentz invariant. One of the main tasks there is to prove the invariance of phase space d^3q \ d^3p and I am trying to prove it with symplectic geometry. I am following Jorge V. Jose and Eugene J...

During the fall, I supose it should stay at rest?

Ok, that does not seem right. :) So I must change the momentum conservation also? I am not sure what exactly changes?

Doesn't say anything about that, so I would assume that it is elastic?

Homework Statement We release m_o = 1 kg object from h=1m height. How much does the Earth move (x)? I just need the comfirmation if I did correctly? Homework Equations Conservation of momentum: m_o v_o + m_E v_E = 0 The Attempt at a Solution I wrote the energy conservation law as (beginning...

Ok, thank you very much blue_leaf77 for all your help and patience with me. Today I passed the Introductory quantum mechanic exam, pretty much because of your help at all my posted exercises. I would really like to thank you also for all your time you took for me, because I know how much time I...

Uf, yes, I was wrong, I don't know what was I doing, I edited it now, so its correct. But anyway, what now, when I have to write |S_{1z};1\rangle|S_{2z};-1\rangle for example, there are 9 elements, at |S_{1z};1\rangle|S_{2z};0\rangle there are 6 and at |S_{1z};1\rangle|S_{2z};1\rangle nine...

Do I have to normalize this matrix from my previous post first? Because if I write |S,m_z\rangle =|1,1\rangle = {1 \over 2} |1,S_x=1\rangle + {1 \over 2} |1,S_x=0\rangle + {1 \over 2} |1,S_x=-1\rangle its not? Or am I wrong again?

Yes, I know, I was confused. :D Aha, I have already tried with the S_x matrix before, to write its inverse. So firstly, I have to write S_x matrix, then find its eigenvectors, build another matrix from this eigenvectors and then find the inverse: \left( \begin{array}{cc} {1 \over 2} & -{1...

Aha, I just didn't know how to write |S,m_z\rangle as a basis, so I only choose (1,0,0),(0,1,0),(0,0,1). So |S,m_x\rangle = \alpha |S,m_z\rangle would be: \begin{align*} |1-1\rangle &= {1 \over 2} |11\rangle - {1 \over \sqrt{2}} |10\rangle + {1 \over 2} |1-1\rangle \\ |10\rangle &= - {1...

Ahaaa, so I was thinking wrong. I have to apply an operator S_x on every |S,m_z\rangle state and then write a matrix, so: \begin{align*} S_x|1,1\rangle &= {\hbar \over \sqrt{2}} |10\rangle \\ S_x|1,0\rangle &= {\hbar \over \sqrt{2}} \big(|11\rangle +|1-1\rangle \big)\\ S_x|1,-1\rangle &= {\hbar...

I think I wil need more help and hints here. So I am thinking this way: \begin{align*} |S,S_z\rangle&=\alpha |S,S_x\rangle\\ |1,1\rangle &= |10\rangle \ \ \textrm{because the z component is 1, x and y must be 0 - right thinking?}\\ |1,0\rangle &= {1 \over \sqrt{2}} \big(|11\rangle +|1-1\rangle...

So if I understand this correctly, I must use first S^2 on my wavefunction to get \langle S^2\rangle and just two times S^2 on wavefunction to get \langle S^4 \rangle. If I do this, I get: \begin{align*} \langle S^2 \rangle &= \langle \psi|S^2|\psi\rangle=4\hbar^2,\\ \langle S^4 \rangle &=...

We measure the S^2 of both particles together, so because of that, I tried to write my wavefunction in |S,m\rangle form. Is this right? Yes, sorry, I made a mistake when I was copying it from my handwriting. I forgot a |10\rangle state, so the whole function is: |\psi_{12}\rangle={1 \over...