Recent content by christianjb

I'm only being a little facetious if I point out that the sum is asymptotically equal to e^N. Want more accuracy? It's better approximated by e^N-[x^(N+1)]/(N+1)!

I may be missing the scampi for the bees, but those aren't vectors, they're parametric eqn's, which describe surfaces. Solving these equations is equivalent to finding the intersection of the three surfaces. I count 6 unknowns and 3 eqns, in which case the solution will be a 3D relation.

Let's not forget Nernst's beautiful proof that there is no 4th law of thermodynamics. Three people developed the 1st law, it took two people to develop the 2nd law, and Nernst was the sole originator of the 3rd law. Thus, there can be no 4th law, because it would have to be developed by zero...

Good question. A particle in a well has a momentum distribution even at T=0 (obtained from the magnitude squared of the FT of the wf). The puzzle then, is how can a particle have a non-zero momentum at zero temperature? A partial answer is that the uncertainty principle puts a constraint on...

You've got a calculator right? See what happens when a=1, and x=1,10,100,1000, etc. Write down the answer and see if there exists a limit. You might actually have fun.

Thanks. That sort-of makes sense. OK, I give in! I'll accept that in common usage, a horizontal asymptote is not regarded as the same sort of beast as a stationary point. (This problem came up in a tutorial I was giving to an undergraduate. I'm a physicist, not a mathematician, and I want...

1) Thanks for the reply. I think half my problem is being confused over the strict technical definition of terms. But yes, that's very clear, I was wrong about the definition of 'critical points'. 2) So, the normal domain of functions is assumed to exclude those nasty infinities? But...

1) Hmm, well then I don't understand what a critical point is. It was my understanding that a critical point is the point at which the derivative is zero. 2) Of course, I understand that it never actually reaches the stationary point for finite values of x, but what would a mathematician...

I'm perpetually confused on this topic. i) We all know that stationary points in 1D are either minima, maxima or inflection points, but consider y=|x|. x=0 is not a stationary point, and yet it is clearly the point at which y is the smallest. Am I technically correct in calling x=0 a...

You beat me by seconds!

int[1/x]=ln(x); ln(1)=0 by definition. It follows that d/dx ln(x)=d/dx(int[1/x])=1/x. See: http://en.wikipedia.org/wiki/Natural_logarithm

The extension and the length are the same things in this case. I'm assuming that the equilibrium length is zero, since no extra information is given. You can see that the length must be in the energy term somewhere, because it obviously costs energy to increase the length.

A distance l-x3 corresponds to a quadratic pe term of k/2 (l-x3)^2.

There are four distances involved in the sum. Taking L to be the length between ends x1-0 x2-x1 x3-x2 L-x3 So, you need an L in your eqn somewhere.

CAH: I think you're misinterpreting V's POV and running the risk of sounding a little pompous. (Sorry, but writing 'science' in capital letters doesn't convince me of your argument.) Everyone has different interpretations of QM, but we're all using the same equations. (I think that was V's...