Recent content by Unkraut

Oh, my bad. I overlooked that. Sorry for my smug reply. May the force be with you.

Interesting. A rather simple question and two pages of theoretically dubious digressions about mathematical theory which don't address the question, except for that one useful answer by romsofia: Yeah, just to expand on this (taking care of x=0) you just try to calculate...

Hello! I'm a math student, currently trying to write my diploma thesis. My field of study is complex dynamics (iteration of holomorphic/meromorphic functions, Julia sets and stuff). It's a farfetched idea, but currently I'm curious about a potential physical interpretation of the things I'm...

Sorry, I was talking about integrating over the whole (1-dimensional) space here (which has the physical dimension of length). And the total probability (of an physical wave function, not the example I used) should be 1. But I see that my example e^ikx is not an example for a real wave function...

Hello! I study mathematics and am in my sixth year, but... I have a very elementary question: I stumbled upon it while learning for quantum mechanics. But it's nothing new, it's happening to me all the time: I get confused by things like this! Observe the following facts: Suppose we...

Maybe my question was a bit unclear. My problem is the following: We have an operator L_+ and an operator L_- such that for a simultaneous eigenvector \psi of L^2 and L_z with eigenvalues \lambda and \mu correspondingly we have: L_zL_+\psi=(\mu+\hbar)L_+\psi and L_zL_-\psi=(\mu-\hbar)L_-\psi...

Hi! I don't know much about QM. I'm reading lecture notes at the moment. Angular momentum is discussed. The ladder operators for the angular-momentum z-component are defined, it is shown that <L_z>^2 <= <L^2>, so the z component of angular momentum is bounded by the absolute value of angular...

This is probably a very stupid question as usual. I don't understand the Lippmann-Schwinger equation. First we have the Schrödinger equation (H+V)\psi=E\psi, and we just rearrange it to \psi=\frac{1}{E-H}V\psi. But now, somehow magically this becomes \psi=\phi+\frac{1}{E-H}V\psi where \phi is...

Ah, I see. It's not \vec r but \hat r, i.e. the unit vector in radial direction. I misinterpreted the notation. Right?

Homework Statement I'm supposed to calculate the scattering amplitudes of some spherically symmetric potentials in the Born approximation and just trying to figure out how that works in general and what a scattering amplitude is actually. Homework Equations 1+1=2 The Attempt at a...

Ah, yes, I confused the angles. Thank you very much! Now it's even more plausible. But still somehow I'm not quite satisfied. Anyway if I wanted to have a mathematically rigorous understanding of it that would probably involve some work. I don't like work. Thank you all for your answers.

Hmm, no, I can't. But I can say that it's plausible... Hmm... probably I'm very stupid: \int_V\nabla^2\frac{1}{r}dV=\int_{\partial V}\nabla(\frac{1}{r})\cdot \vec n dS=\int_{\partial V}(-\frac{1}{r^2})dS=\int\limits_0^{2\pi}\int_0^{\pi}(-\frac{1}{r^2})r^2sin\phi d\theta d\phi =...

\nabla^2(\frac{1}{r})=\frac{1}{r^2sin\theta}(sin\theta\frac{\partial}{\partial r}(r^2\frac{\partial}{\partial r}(\frac{1}{r})+\left[\text{derivatives with respect to the angles = 0}\right]) =\frac{1}{r^2}\frac{\partial}{\partial r}(-r^2\frac{1}{r^2}) =\frac{1}{r^2}\frac{\partial}{\partial...

Homework Statement Prove that \nabla^2(\frac{1}{r})=-4\pi\delta^{(3)}(r), where \delta^{(3)} is the three-dimensional Dirac delta function. Homework Equations 1+1=2 \pi=3 The Attempt at a Solution I am very confused. I don't see how this statement can be true. Deriving an...

Oh, now that you say it, that seems reasonable. Thank you! In quantum mechanics I always have problems determining what kind of reasoning is actually reasonable :)