Recent content by devd

1. Probability of spin-flip due to scattering

Homework Statement A beam of spin-1/2 particles scatters off of a target consisting of spin-1/2 heavy nuclei. The interaction between the particle and nucleus is given by $$V(\vec{ r})= V_0~\delta (\vec{r})~ \vec{S}_1. \vec{S}_2$$ 1) Averaging over initial spin states, find the differential...
2. I Transpose and Inverse of Lorentz Transform Matrix

Indeed, ##\Lambda^{-1}=g^{-1}\Lambda^T g ~##. But, for the Minkowski metric tensor, ##g^{-1}=g##, since ##g^2=1.## Ok, so my basic confusion, distilled to its essence is thus: Using the earlier derivation, we see that ##(\Lambda^{-1})^\rho{}_\beta=\Lambda_\beta{}^\rho##. Tung's definition of...
3. I Transpose and Inverse of Lorentz Transform Matrix

Oops, sorry! I meant, $$g_{\mu\nu}=g_{\alpha\beta}\Lambda^\alpha{}_\mu\Lambda^\beta{}_\nu\\ \implies\delta^\rho{}_\nu=g^{\rho\mu}g_{\mu\nu}=g^{\rho\mu}g_{\alpha\beta}\Lambda^\alpha{}_\mu\Lambda^\beta{}_\nu\\ \implies \delta^\rho{}_\nu=\Lambda_\beta{}^\rho \Lambda^\beta{}_\nu$$ Now we write...

12. Schools UMass Physics vs CWRU Astronomy

I have offers from UMass Amherst Physics and Case Western Astronomy for their respective Phd programs. I'm having a tough time deciding between the two. Leaving aside the differences due to astronomy vs physics, what other factors are important to consider while making a decision? UMass Physics...
13. Average number of particles/subsystems in a state

The given options only makes sense if by 'system' they mean ensemble and by 'subsystem' they mean members of the ensemble. Then, ##P(E_1)= \cfrac{e^{-\beta E_1}}{e^{-\beta E_1}+e^{-\beta E_2}}## Again, ##P(E_1)= \cfrac{N_1}{N_0}. ## Therefore, ##N_1 = N_0\left(\cfrac{e^{-\beta E_1}}{e^{-\beta...
14. Average number of particles/subsystems in a state

Homework Statement A system in thermal equilibrium at temperature T consists of a large number of subsystems, each of which can exist only in two states of energy and , where . In the expressions that follow, k is the Boltzmann constant. For a system at temperature T, the average number of...
15. Variation of system energy in Canonical Ensemble

Yes, i think i get where i was going wrong. I was equating the thermodynamic notion of internal energy to the internal energy of one individual system, instead of the ensemble average. Thanks for the reply. Just to be clear, there are multiple microstates with different U which correspond to...