Recent content by Lunar_Lander

I think I got <V>, the first solution I posted was from the indefinite integral. A^2\frac{e_0^2}{\epsilon_0}\int_0^{\infty}\exp(-2\alpha~r)r~dr A^2\frac{e_0^2}{\epsilon_0}\cdot\frac{1}{4\alpha^2}=\frac{e_0^2\alpha}{4\pi\epsilon_0}. Also, A can be found by normalizing the original wave...

I think I got it now. First of all I learned that the 2p energy level is degenerate, thus m should have no influence on it and there is only one calculation to do for 2p. Then I tried to calculate 1s: \psi_{1s}=\frac{1}{\sqrt{\pi}}(\frac{Z}{a_0})^{3/2}\exp(-\frac{Zr}{a_0}) As we are...

I also attempted a run at the 2p (for m=0) and it looks like this: \psi_{2p_0}^2=\frac{1}{32\pi\cdot a_0^5}\cdot r^2Z^5\exp(-\frac{2Z\cdot r}{a_0})\cdot\cos^2(\theta) <r>=\frac{1}{32\pi\cdot a_0^5}\int_0^r \int_0^{\pi} \int_0^{2\pi} r^2Z^5\exp(-\frac{2Z\cdot...

Homework Statement Determine for the hydrogen atom states 1s and 2p the expectation value of the radius r and the associated mean square error Δr. Homework Equations Wave Functions for 1s and 2p from Demtroeder's Experimental Physics Volume 3 (it says "The normalized complete...

Sorry, I had once seen this notation (T=\frac{\hbar}{2m}\Delta) somewhere. Would it rather be: <T>=-\int\int\int r^2\cdot\sin(\theta)\cdot\psi^2\cdot\frac{\hbar}{2m}\Delta\psi~dr~d\theta~d\phi ? I'll try the limits later on, but thanks for the help already :)!

So, I am getting this: -4\pi\cdot A^2\frac{e_0^2}{4\pi\epsilon_0}\int \exp(-\alpha\cdot r)\cdot r~dr -A^2\frac{e_0^2}{\epsilon_0}\int \exp(-\alpha\cdot r)\cdot r~dr and A^2\frac{e_0^2}{\epsilon_0}\cdot \frac{1-\exp(-\alpha\cdot r)\cdot (\alpha\cdot r+1)}{\alpha^2} Is this correct? If...

Thank you Vela! Would it maybe be possible for one of you to show me just how to correctly do this calculation, because my problem is that I usually need a good example and explanation on how to calculate complex things. When I look at calculations in books, those are usually good, but when I...

"Optimizing" a Wave Function Homework Statement Consider a Hydrogen Atom, an electron in an attractive Coulomb potential of the form V(r)=-\frac{e_0^2}{4\pi\epsilon_0r}, where e0 is the elementary charge. Assume the following wave function for the electron (with α>0): \psi(r)=Ae^{-\alpha...

Homework Statement Consider a potential well with infinite high walls, i.e. V(x)=0 for -L/2\leq x \leq +L/2 and V(x)=\infty at any other x. Consider this problem (the first task was to solve the stationary Schroedinger equation, to get the Energies and Wave Functions, especially for n=1 and...

Ah, thank you! When I take the complex conjugate of ψ for taking the square, then I get \rho(x,t=0)=\frac{1}{\sqrt{2\pi}d}\exp[-\frac{(x-x_0)^2}{2d^2}]. Looks like a gaussian bell curve to me from the form of the equation. Could that be it?

An addendum, just received an E-Mail from the professor, who said that due to many people having difficulties, he would give the solution for ψ, and he said it looks like this: \psi(x,0)=\frac{1}{\pi^{1/4}\cdot 2^{1/4}\cdot d_0^{1/2}}\exp[i\cdot k_0(x-x_0)]\exp[-\frac{(x-x_0)^2}{4d_0^2}]...

Homework Statement Consider the time-dependent one-dimensional Schroedinger Equation for the free particle, i.e. let the Potential be V(x)=0. Consider a wave packet, i.e. \psi(x,t)=\int_{-\infty}^{\infty}=A(k)\exp[i(kx-\omega(k)t]dk. Consider especially the Amplitude distribution...

For clarification, here is a picture of the system I am asking about.

Homework Statement An object at a distance a1 in front of a convex lens with the focal length f1 is imaged at a distance b1. A second lens at the distance d from the first lens with the focal length f2 is then imaging this Image with the image distance b2. a) Give the image distance b1 as...

OK, thanks :)! In the metal, there should be a shift of charges due to the field from the inside, so that the inside of the metal layer is free of the electric field, i.e. |E(r)|=0? One last pointer on the fields inside though, please. Do I need to incoporate the radius of the glass sphere...