Recent content by lonewolf5999

Ok, thanks for the reply!

Consider a universe where the intrinsic spin of the electron is S = 5/2, but all other parameters and Rules of Quantum Mechanics are the same. Find the degeneracy of the n=1 and n=2 levels of hydrogen. My understanding is that electrons in an atom have 4 quantum numbers n,l,ml,ms, and different...

After trying your suggestion with z1 = 1 + i, z2 = -1 - i, and f(z) = 1/((z - z1)*(z-z2)), I ended up with the integral over the imaginary axis being the negative of that over the real axis, so I located my poles on the line y = -x instead, and that solved the problem. Thanks for the help!

I'm looking for a function which has two simple poles, and whose integral along the positive real axis from 0 to infinity is equal to its integral along the positive imaginary axis. I don't really know where to start. I'm looking at functions which have symmetry with respect to real/imaginary...

Ok, thanks very much for the help and the quick reply!

Thanks for the reply. I hope you can clarify a couple of points in your answer, however. When you say "We have a continuous function f(x)=d(x,F)," am I correct in saying that you mean d(x,F) = inf{d(x,f): f lying in F}? Also, what do you mean by ]-1/n,1/n[ ? Is it something like an open...

This is not a homework problem, just something I was thinking about. In a general metric space, is it true that every closed set can be expressed as the intersection of an infinite collection of open sets? I don't really know where to begin. Since the finite intersection of open sets is open...

I can't find that theorem in my book, but if I use it, the answer comes out very easily: since f+ig is analytic and non-zero on Ω, let H be an analytic function such that f+ig = exp(H), then define h = iH, and I can show that f = cos(h), g = sin(h). I guess I'll just prove it for my problem...

Here's the problem: Let f and g be analytic functions on a simply connected domain Ω such that f2(z) + g2(z) = 1 for all z in Ω. Show that there exists an analytic function h such that f(z) = cos (h(z)) and g(z) = sin(h(z)) for all z in Ω. Here's my attempt at a solution: f2 + g2 = 1 on Ω...

Thanks for the replies!

I'm working on a problem for my analysis class. Here it is: Let f be differentiable on an open subset S of R. Suppose there exists M > 0 such that for all x in S, |f'(x)| ≤ M, i.e. the derivative is bounded. Show that f is uniformly continuous on S. I'm not too sure that this question is...

Okay, I think that clears up the confusion I had. Thanks for helping me out.

I'll just post the book's answer to this question and see if anyone has any thoughts on this as well. "Let A be a bounded set, and let s = sup A. Then for any ε > 0, s - ε is not an upper bound, so we can find an element a of A such that a > s - ε. Hence a lies in the ε-neighborhood of s, and...

I'd agree with you, except that my book also says that x is a limit point of a set A iff there exists a sequence (an) contained in A such that lim an = x, and an =/= x for all n. So this means that when looking for a sequence contained in A converging to x, we're not allowed to consider the...

Hello, I'm working through an analysis textbook on my own, and came across a true/false question I was hoping someone could help me with. The question is: If A is a bounded set, then s = sup A is a limit point of A. I think that the statement is false, as I came up with what I think is...