Recent content by Tarantinism

The space of BOUNDED operators on a Hilbert space is itself a Banach space, so it is easy to define the usual Fréchet derivative: http://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative I wouldn't know how to define this derivative, on the other hand, if you map into some unbounded operators...

Hej! Try to have a look at this: http://en.wikipedia.org/wiki/Bochner_integral Hej daº

Hi, VortexLattice Try with the mixed state 1/3|\psi_1 >< \psi_1|+1/3|\psi_2 >< \psi_2|+1/3|\psi_3 >< \psi_3| and take the trace of the product with |\delta_x >< \delta_x | Do not try with any pure state ;)

There are sooo many. Marsden-Hoffman for example? do you know¿

You are getting the most classical interpretation (due to Drude-Lorentz) :) http://en.wikipedia.org/wiki/Drude_model When you get more acquainted with this stuff, get prepared to all the new surprises in the form of quantum mechanics' laws consequences. Intuition can only explain the very...

Is usually easier: 1. The distance is 0 if the planes are not parallel. 2. When they are parallel, they have a common unit normal vector. Take any vector joining any point of the first plane with any point of the second plane and the scalar product with that normal vector. This gives the...

No, that is x multiplied by the derivative of f, you cannot simplify more.

Ahh, i forgot that was indeed the free hamiltonian, then seems obvious. I have my scattering theory rusty, damn it.

Nobody? It seemed to be a good question. My point of view: I guess the reason is to avoid more singularities, as could be the case of continuous spectra. Knowing that the limit \epsilon \rightarrow 0 would be the same in all directions (imaginary, real or "mixed complex") There are no...

And, VortexLattice, keep in mind, that when you add electrons, you cannot know "which" electron has m=-1 , m=0 or m=1, they spread in such antisymmetric tensor product so that every electron can be in any orbital with the same probability (fermions indistinguishability) |\psi_1> \otimes...

Actually, if you sum all the probability distributions, for example, the three distributions from those eigenfunctions for l=1, it gives an actual spherically symmetric function. Your intuition is good, there is no Z axis. Without any external fields, an electron with l=1 would be 1/3 in each...

I think that you can follow Eisberg-Resnick just after you have studied a elementary physics semester, of course not in detail. Its level is not very higher than Scientific American's. On the other hand, it is not enough even for a second year university course, at least in my university.

cos2x = (1+cos(2x))/2 Integration leads to 0,5 (averaged over the lenght)

There is a middle-"pseudoproof" at half the way (excuse me if my english is not very good). That is the semiclassical theory. Based on the ancient quantum physics and the Sommerfeld-Wilson quantization rules for bounded motion. The different numbers of l, for example, would give the only...

Hi jd! yenchin's link is quite good. As he says, it comes from the very definition. They key is just to understand the definition, from discrete sums to continuum (integral) in the limit. I think there is no general rule, no "mechanical" way. Go to the definition and set this sum as a Riemann...