Recent content by Fosheimdet

How is it a total derivative though? Isn't ##\frac {\partial}{\partial x^j}## a partial derivative? Also, why can you make the assumption that the function goes to zero at infinity?

In my QFT homework I was asked to prove that $$\int d^3x \int \frac{d^3k}{(2\pi)^3} e^{i\mathbf{k} \cdot (\mathbf{x} - \mathbf{y})} k_j f(\mathbf{x}) = i \frac{df}{dx_j}(\mathbf{y}) $$ Using ##\frac{\partial e^{i\mathbf{k} \cdot (\mathbf{x} - \mathbf{y})}}{\partial x^j} = i k_j e^{i\mathbf{k}...

I see. The ##\vec r'## will simply shift the origin of ## f(\vec r) = e^{i\vec q \cdot (\vec r-\vec r')} \frac{Q}{4\pi |\vec r-\vec r'|} ## and because the integral limits are ##-\infty## and ##+\infty##, the integral will be the same for every value of ##\vec r'##. We can therefore set ## \vec...

I'm reading through Thomson's "Modern Particle Physics", and I've gotten stuck at a point in the derivation of the form factor for electron scattering in a static potential due to an extended charge distribution. It's just a mathematical "trick" i don't quite get. He goes from $$\int\int...

I'm looking through an old exam, and don't quite understand the solution given for one of the problems. We have given a wavefunction g(\phi,\theta) = \sqrt{\frac{3}{8\pi}}(-cos(\theta) + isin(\theta)sin(\phi)) and are asked what possible measurements can be made of the z-component of the...

While reading the derivation of the formula \lambda' - \lambda = \frac{h}{ m_ec}(1-cos(\theta)) on Wikipedia, they point out that the momentum gained by the electron is larger than the momentum lost by the photon: $$ p_e=\frac{\sqrt{h^2(\nu-\nu')^2 +2h(\nu-\nu')m_ec^2}}{c} >...

T/V. You have my gratitude. I will now shed a tear for all the sleep this trivial thing has cost me.

Yes, but p is constant as indicated by the subscript in \frac{\partial T }{\partial V}_p.

I have been tearing my hair out for a while over a step in the proof of the relation pV^{\gamma}=constant. The textbook has assumed that we are dealing with an ideal gas undergoing an adiabatic process. Therefore dQ=0 and we get $$C_vdT + (c_p-c_V)\left(\frac{\partial T}{\partial...

If $$f(z)=u(x,y)+iv(x,y)$$ is analytic in a domain D, then both u and v satisfy Laplace's equations $$\nabla^2 u=u_{xx} + u_{yy}=0$$ $$\nabla^2 v=v_{xx} + v_{yy}=0$$ and u and v are called harmonic functions. My question is whether or not this goes both ways. If you have two functions u...

Thank you so much! Great explanation, made things allot clearer.

A theorem in my textbook states the following: For every n=0,±1, ±2, --- the formula ln z=Ln z ± 2nπi defines a function, which is analytic, except at 0 and on the negative real axis, and has the derivative (ln z)'=1/z. I don't understand why the logarithm isn't analytic for negative real...

Homework Statement Let A be a nxn matrix, and I the corresponding identity matrix, both in the real numbers ℝ. Assume that A^m=0 for a positive integer m. Show that I-A is an invertible matrix. Homework Equations The Attempt at a Solution

Yes they do collide head-on. And the Photons afterwards have opposite directions. But still the absolute value of the momentum has increased after the collision. Isn't this against the laws of physics?

Homework Statement An electron and a positron is on a collision course. Both have a speed of 1,80*10^8 m/s. What are the frequencies of the two photons created after the electron and the positron has annihilated? Electron mass=positron mass= 9,11*10^-31 kg Homework Equations...