Recent content by Mantella

So, even though the expansion occurs at z=infinity it is still technically accurate around the singularity of z=0 because I am hypothetically using an infinite number of terms? If I actually wanted to accurately evaluate the function around the singularity I would need to go to very high power...

Question 1. a) here -> http://www.math.ubc.ca/~sjer/math300/s7.pdf. I found a variety of other sources saying the same thing just by googling "laurent series of cos(1/z)". If this is wrong then how would I construct a Laurent series for \cos{\frac{1}{z}} such that I could find it's residue?

Question 1: Find the Laurent series of \cos{\frac{1}{z}} at the singularity z = 0. The answer is often given as, \cos\frac{1}{z} = 1 - \frac{1}{2z^2} + \frac{1}{24z^4} - ... Which is the MacLaurin series for \cos{u} with u = \frac{1}{z}. The MacLaurin series is the Taylor series when u_0 = 0...

Where does the Stern Gerlach term in the Pauli equation come from? Taken from http://en.wikipedia.org/wiki/Pauli_equation. Following wikipedia's steps the Stern Gerlach term pops out when you apply the Pauli vector identity. I don't understand this step. It seems as if there should be no Stern...

One of my homework problems asks what number of photons are released in the decay of ortho- and para-positronium, and I'm somewhat confused. From the point of view of 4 momentum conservation I understand that at least two photons must be emitted in the decay process. In the case of...

Whoops. Got spherical polars wrong. That's embarrassing. Thanks for the help!

I kinda see what you're getting at, but still struggling a bit. Intuitively, I see the path from infinity to r as being a negative path (moving in a path against a field), but am I simply adding a negative that is already supplied by the integral? What I got from what you said is this...

I've been having a problem with the sign of potential. Electric potential as I know it is defined as V = -\int_{C}\vec{E}\bullet\vec{dl} where C is the path from a location defined as zero potential to the location you are measuring the potential at. Now I want to run through this really quick...

I see what your saying, but what about in a situation like 2:32 in a video on youtube titled Gyroscope by ScienceOnline (sorry but I can't post links yet) The frame around the gyroscope isn't moving (probably because friction from the string is keeping it from moving), and because of this the...

I was hoping someone could clear this up for me. I've been thinking about it a bit, and I am thoroughly confused. Here is what I have come up with so far. The situation: A horizontal (wheel vertical) gyroscope spinning counter clockwise held up at one end by a string. Now change views so...