Recent content by yaychemistry

I kind of have a follow-up question to JayFsd (a year later, ha). Suppose that a is complex and you have the integral \int_C f\left(x\right) \delta\left(x - a\right)dx such that a lies on the countour C, you would expect the result to be: \int_C f\left(x\right) \delta\left(x -...

Hi, First, thank you for reading this. I've got a complex function, F(z), which is assumed to be analytic, and I know it's values along a contour in the complex plane. Say, for simplicity, that contour is known parametrically as x(t) = cos(t), y(t) = sin(t), 0 < t< pi, thus I know F(x(t) +...

Right, so its harder to decouple angular momenta than the couple them together and it involves use of Wigner 3-j symbol's, or at least very careful application of the CG coefficients and I can't remember it right now. Instead let's take a physical approach: We know that the TOTAL angular...

that looks like the right step. I would suggest two different strategies for each term in the integral then. The first one looks like a u-substitution. The second looks like one of those gross inverse trig function anti-derivatives, see if you can look them up.

Hi, it's been a little while since I've dealt with Term symbols and the CG coefficients, but here goes (e.g. I may be totally wrong, but at least this might get you thinking about the right answer): The term symbol we're shooting for the ^4\textrm{D}_{1/2}, so for our spin we need the coupled...

Hello again, I think I should clarify what I was trying to say earlier with an example. Let's say an electron has 0.00010% more charge than a proton e.g. a proton has a charge of +1q and the electron has a charge of -1.0000010q. If I take a proton and an electron together (perhaps bind them...

That is the correct wave function. Can you use that to predict the probability in being in one section of the box? Remember that \left|\psi\left(x\right)\right|^2 is a probability density, so you have to integrate over some interval in x (The right interval is specified in your problem, can you...

Do you know the wave function for a particle in a box, or can you try to derive them?

Hello, I think there are other solutions. Take your equation, x\psi\left(x\right) = \lambda\frac{d}{dx}\psi\left(x\right) and substitute \psi\left(x\right) = \exp\left(f\left(x\right)\right) and see if you don't get an equation for f\left(x\right) which has a solution that depends on...

Hi aforce20, Do you remember how Power defined? It's the amount of energy used per unit time. Perhaps that will help you with the first problem. For the second problem, are you familiar with the concept of conservation of energy? The formula for kinetic energy us E_\textrm{kinetic} =...

Hello ZoroP, I think the crux of this problem is to explain WHY we know that the proton and electron each have the same charge. If they differed, as the problem suggest we pretend, then there would be a measureable force. The 0.00010% is the pretend difference in charge between the electron and...

Hello mju4t You've got it right, you have to integrate it piecewise. That's how the function is defined. Good luck.

Hello dron, If I could, I would like to know what your motives are in discovering these "irrational" pieces of Quantum Mechanics are. It seems to me you are not just trying to satisfy an idle curiosity, but are looking for ammunition to take us scientists down a peg, e.g. This might be...

The way I see how to Variational principle works in the Roothan equation, or in Raylieigh-Schrödinger perturbation theory, etc in order to find both gound and excited states (at least in 1-particle Hamiltonians) is this: We agree that the variational principle makes sense that one could find...

The usual approximation is the Taylor series: f\left(x\right) \approx \sum_n \frac{1}{n!}\left.\frac{d^{n}f}{dx^{n}}\right|_{x=a}\left(x - a\right)^n However, your function (due to the power pi/e) does not look exactly like a Taylor series. My best guess is that it's the Taylor series of...