Recent content by Brian-san

I checked my notes and it's supposed to come out to \frac{du_\mu}{ds}=\frac{q}{m}F_{\mu\nu}u^\nu We've been using the convention that the spatial terms have the minus signs in the Minkowski metric (+---). In an earlier step I used u_\mu=\eta_{\mu\nu}u^\nu to get the lower mu index in the...

Homework Statement Show that the Lorentz force law follows from the following variational principle: S=\frac{m}{2}\int\eta_{\mu\nu}u^\mu u^\nu ds-q\int A_\mu u^\mu ds Homework Equations Definition of Field Strength Tensor Integration by Parts Chain Rule & Product Rule for Derivatives The...

1. Homework Statement : Consider a two dimensional Minkowski space (1 spatial, 1 time dimension). What is the condition on a transformation matrix \Lambda, such that the inner product is preserved? Solve this condition in terms of the rapidity. 2. Homework Equations : Rapidity Relations...

So if we apply Stirling's approximation...

The oscillators can have energy in amounts of \hbar\omega, 2\hbar\omega, ... k\hbar\omega, the only constraint being that the total energy of all oscillators is E. m_1 is counting the number or oscillators with energy \hbar\omega, similarly for the other m's. For example say we had 6...

Homework Statement a) Derive an asymptotic expression for the number of ways in which a given energy E can be distributed among a set of N, one-dimensional harmonic oscillators, the energy eigenvalues of the oscillators being (N+\frac{1}{2})\hbar\omega, n=0, 1, 2, .... b)Find the corresponding...

I got L=2 from the fact that particle A is spin-3/2 and the total angular momentum for the resulting particles is some total orbital angular momentum L, plus the spin from the spin-1/2 particle. Since the total angular momentum is conserved, I went with 3/2=L±1/2, which gave L=1, 2. The I...

I'm pretty sure the answer from the book is just a rearranged form of your equation y = e-3t ( C1 ( cos(2t) + i*sin(2t) ) + C2( cos(2t) - i*sin(2t) ) ) Just multiply out everything, then you can factor the sine and cosine terms, so it's of the form e-3tcos(2t)+e-3tsin(2t). The rest is just...

Thanks, everything makes more sense for part one now. It's always the sings on the numbers that would throw me off, when to use ±, when to only keep positive values, etc. In 2, why would the resulting particles not have their own individual orbital angular momentum? Assuming there is only...

The main trick with this solution method is that you can rename the indices. In this case you change the index in the final sum so it matches the first two terms. Let n=n-2, then the lower index on the sum is n=2 and the third term is 10\sum_{n=2}^{\infty}a_{n-2}x^{r+n} Now you can pull out...

Homework Statement 1. Consider a deuterium atom (composed of a nucleus of spin I=1 and an electron. The total angular momentum of the atom is \vec{F}=\vec{J}+\vec{I}, the eigenvalues of J^2 and F^2 are J(J+1)\hbar^2 and F(F+1)\hbar^2 respectively. a) What are the possible values of the quantum...

Homework Statement a) Consider a conducting sphere of radius R whose surface is maintained at a potential \Phi(R)=\Phi_0cos\theta. Assuming that there are no charges present (inside or outside), what is the potential inside and outside the sphere? b) Consider a cylindrical conducting can of...

I solved the equations again, separately for each region and took a few ideas from my notes when thinking about the boundary conditions at the walls of the well. Without going through that whole process, I got: \psi_1(x)=A_1sin(k(L-x)), 0<x\leq L \psi_2(x)=A_2sin(k(L+x)), -L\leq x<0 With the...

Then is this solution from a previous post correct? \psi(x)=L^{-\frac{1}{2}}sin\left(\frac{n\pi}{L}x\right), E_n=\frac{n^2\pi^2\hbar^2}{2mL^2} It satisfies that the wave function is zero at x=0,L,-L, is normalized and satisfies the Schrödinger equation. Also, the last few parts ask about...

Depending on the substitution used, at least 2 times.