Recent content by Rubiss

Thanks for the reply! I will try to work through everything you have written. By the way, your assumption ##\small |C_{\alpha+}|^{2}+|C_{\alpha-}|^{2} = 1## is correct because the operators were constructed from a unitary transformation.

Ok...if I write out the original order (product, sum, product), I will still get zero \begin{align*} \prod_{p}\sum_{p'}\prod_{p''}\delta_{pp'}\delta_{p'p''} &=\prod_{p}\sum_{p'}\delta_{pp'}\delta_{p'1}\delta_{p'2}\delta_{p'3} \delta_{p'4} \\...

0 0. I'm still not seeing how I am going to get the value of 4 I need. Let me show you what my problem is \begin{align*} \prod_{p} \prod_{p''} \sum_{p'} \left( \delta_{pp'} \delta_{p'p''} \right) &=\prod_{p} \prod_{p''} \left( \delta_{p1}\delta_{1p''} + \delta_{p2}\delta_{2p''} +...

They must be equal... I know that. I'm trying to be very explicit in all my steps though. So if the kronecker deltas say p=p'=p'', how does that affect the products?

Homework Statement I am trying to calculate the expectation value of an operator in the Lipkin model of nuclear physics. The background isn't important because my problem in really just a math problem. Homework Equations The anticommutation relation \begin{align*} a_{p\sigma}...

Homework Statement I'm currently trying to understand linear and circular polarization of electromagnetic plane waves. Let's say I have an electric field given by \vec{E}=Acos(kx-\omega t)\hat{x}+Bcos(kx-\omega t - \gamma)\hat{y} A is given and nonzero. I want to find what values of...

I'm well aware of that. I calculated the dot product above in component form: I resolved q into x and y components and the vector r into its components for eacf particle. Particle 1 had a x component of a/2 and a y component of a/2, particle 2 etc. Calculating the dot product your way does not...

Homework Statement Given that the scattering amplitude off of a single atom is f_{1}(\vec{q}), find the scattering amplitude for 1) four atoms each placed in the corner of a square of length a, and 2) two atoms a distance d apart Homework Equations The total scattering amplitude can...

Ah, yes! That is the crucial part I was missing - del acts on both psi and A. Thanks so much!

I think you're right, but I have rewritten my steps many times, and do not get that factor of 2 to show up. Very frustrating.

Homework Statement Derive the continuity equation for a charged particle in an electromagnetic field Homework Equations The time-dependent Schrödinger equation and its complex conjugate are i\hbar\frac{\partial \psi}{\partial t}=\frac{1}{2m}(-i\hbar \vec{\nabla} - \frac{e}{c}...

Ok. Since I'm not receiving any help. Let's try again. Let me me start with a different problem (that I found in a problem book) for which I know the solution: A particle of mass m is projected from infinity with a velocity vo in a manner that it would pass a distance b from a fixed center of...

Homework Statement I'm taking a graduate level course in classical mechanics that uses Goldstein's book. We are currently discussing scattering in a central field in chapter 3. Here are two problems that might be very basic/standard scattering problems, yet I'm not how to proceed or get...

Homework Statement Problem 8.1 from the third edition of Introduction to Electrodynamics by Griffiths: Calculate the power (energy per unit time) transported down the cables of Ex. 7.13 and Prob. 7.58, assuming the conductors are held at potential difference V, and carry current I (down one...

The vector S is the sum of its three components, but I don't think the expectation value of the vector S is the expectation value of its three components. That is, I don't think we can take \vec{S}=S_{x}\hat{x}+S_{y}\hat{y}+S_{z}\hat{z} and then take the expectation value of both sides to...