Recent content by Like Tony Stark

I tried using the Wigner matrices: $$\sum_{m'=-2}^{2} {d^{(2)}}_{1m'} Y_{2; m'}={d^{(2)}}_{1 -2} Y_{2; -2} + {d^{(2)}}_{1 -1} Y_{2; -1} + ...= -\frac{1-\cos(\beta)}{2} \sin(\beta) \sqrt{\frac{15}{32 \pi}} \sin^2(\theta) e^{-i \phi} + ...$$ where $$\beta=\frac{\pi}{4}$$. But I don't know if...

I've already calculated the total spin of the system in the addition basis: ##\ket{1 \frac{3}{2} \frac{3}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{1 \frac{3}{2} \frac{1}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{0 \frac{1}{2} \frac{1}{2}}; \ket{0 \frac{1}{2} \frac{-1}{2}}; \ket{1...

Yes, I know that ##\vec{S_1} \cdot \vec{S_2}=\frac{1}{2} [S^2-(S_1)^2-(S_2)^2]##. That means that the energy levels are: $$E=-\frac{\lambda}{2h^2} \delta(x) [s(s+1)-s_1(s_1+1)-s_2(s_2+1)]$$ $$E=-\frac{\lambda}{2h^2} \delta(x) [s(s+1)-\frac{11}{4}]$$ with ##s=\frac{1}{2}, \frac{3}{2}##...

1) The Hilbert space for each particle and the system are: ##H_1={\ket{\frac{1}{2} \frac{1}{2}}; \ket{\frac{1}{2} -\frac{1}{2}}}## ##H_2={\ket{1 1}; \ket{1 0}; \ket{1 -1}}## ##H=H_1 \otimes H_2## 2) I'm not sure what "considering the total Hamiltonian" means, but I think that the two CSCO...

Thanks for your answer! Let's see if I've understood... So, for ##\alpha## I have to calculate ## \frac{\partial V}{\partial T}=\frac{\partial}{\partial T}## ##\frac{-aVT^{5/2}e^{\frac{\mu}{RT}}}{P}##, for constant ##P## Then, for ##c_P##, I have to calculate ##\frac{\partial^2 A}{\partial...

Thanks! I have arrived to ##c_P=\frac{2T^2}{9B^3P}## and ##\alpha=\frac{NT^2}{9B^3P^2V}##. But when I replace this identities in the expression for ##\mu## I get ##\mu=0##

Hello! It's from a purely thermodynamics class. The reference book in my course is Callen's Thermodynamics.

Hi All the expressions for calculating the properties are given in terms of ##S##, ##V## and ##N##. Should I find the energetic representation and then apply the formulas, or is there another way? Then, for finding the energetic representation, I know that ##A=U–TS–\mu N## But I want all these...

Hi ##\mu=\frac{\alpha TV–V}{N c_P}##. So, firstly, I have to calculate ##\alpha## and ##c_P##. So ##\alpha=\frac{1}{V} \frac{\partial V}{\partial T}## at constant ##P##. I can write ##U=PV##, then I replace it in the equation of ##T##, solve for ##V## and then I differentiate with respect to...

I've attached images showing my progress. I have used Maxwell relations and the definitions of ##\alpha##, ##\kappa## and ##c##, but I don't know how to continue. Can you help me?

Ok But apart from the elastic force, is the solution ok?

So should I consider just one degree of freedom?

Maybe I made a mistake, but I think it's possible to write its radial and transversal components using trigonometry

Hi I thought that a bike could be simply modeled as two wheels attached by a rigid bar. If the wheels move without sliding, then there is one degree of freedom: one of the wheels moves and so does the other one since they are rigidly attached by the bar. Then, if the wheels can turn to the right...

Hi I've written D'Alembert's principle as you can see in the attached files. I computed the virtual work done by the weight and the elastic force (since the work done by the normal force is zero) and then I used the fundamental hypothesis, which states that the constraint forces can be written...