809 reputation
221
bio website ziga-lausegger.netau.net/…
location Slovenia
age 27
visits member for 2 years, 4 months
seen Feb 24 at 9:43

I love to program and crosscompile baremetal C programs for ARM based microcontrollers, I love physics and i love writing science documents/books in LaTeX. It amazes me how physics is connecting all science and is helping mathematics to evolve. In order for science profession to comunicate on a high level i advise everyone to use Linux, LaTeX and a good vector imaging program like Inkscape.


Aug
7
asked Moving electron - finding the wavefunction
Aug
7
comment QM - calculating expectation value for velocity of an electron
After looking at @Ali's anwser I believe that you meant "momentum operator" instead of the "velocity operator". Thanks for pointing this out as i wasn't sure if i d get $\langle v \rangle^2$ or $\rangle v^2 \langle$ using the kinetic energy method - i guess it is the later huh - can i ask you, how do we know this? Why do we know that by using the kinetic energy method we get $\langle v^2\rangle$ and not $\langle v\rangle^ 2$? For the solution i will take Ali-s anwser.
Aug
7
accepted QM - calculating expectation value for velocity of an electron
Aug
7
comment QM - calculating expectation value for velocity of an electron
Regarding your 1st paragraph. Why did you use the energy $\langle E \rangle$ and an operator $\hat{H}$ instead of $\langle E_k \rangle$ and an operator $\langle \hat{T}\rangle$?
Aug
7
comment QM - calculating expectation value for velocity of an electron
I will be satisfied with only a magnitude so far ... don-t know enough of QM yet to think about QM vectors :). Do zou think this classical approximation is good enough for a particle in a box. I mean i calculated $\langle E_k \rangle=338.79eV$.
Aug
7
comment QM - calculating expectation value for velocity of an electron
So this is not possible? $\langle E_k\rangle = \tfrac{1}{2}m\langle v \rangle^2 \longrightarrow \langle v\rangle = \sqrt{2 \langle E_k \rangle / m}$
Aug
7
comment QM - calculating expectation value for velocity of an electron
I have discovered that in this PDF they diferentiate the wavefunction over time but i have a stationary state! Do i have to multiply it with $\exp\frac{i}{\hbar E t}$ and then diferentiate it? Is there any easier way if i already calculated expectation value for kinetic energy $\langle T \rangle$?
Aug
7
comment QM - calculating expectation value for velocity of an electron
Never mind I found it in this PDF - page 32 - Now give me some downvotes for being lazy :D
Aug
7
comment QM - calculating expectation value for velocity of an electron
Well i asked this because I cant find an anwser in my book which only describes operators of kinetic energy, potential energy, momentum, position and position square... If i write expectation value for speed, Google returns mostly these same operators...
Aug
7
comment Wavefunction as a combination of two stationary states - how to find those states?
Thank you very much. Ok so if we scalar multiply the stationary state $\phi_i$ with a wavefunction $\psi$ and integrate over $x$ we should get the constant $c_i$ which is normaly in front of an stationary state? How come?
Aug
7
comment Wavefunction as a combination of two stationary states - how to find those states?
Oh i see if there is a cosinus the problem becomes much harder.
Aug
7
asked QM - calculating expectation value for velocity of an electron
Aug
7
comment Wavefunction as a combination of two stationary states - how to find those states?
@Sebastian Henckel I know that if the problem is on an interval $0<x<d$ the solutions are all like $\sin(n\pi x/d)$ but I wondered if i had a problem like this: $\psi= A\left[ \cos \left(\frac{7 \pi x}{d}\right) + \frac{1}{3}\sin \left(\frac{4 \pi x}{d}\right)\right]$ could i reckognize this as a superposition of states on an interval $-d/2<x<d/2$ where in general solutions are of form $\sin(n\pi x/d)$ for even and $\cos(n\pi x/d)$ for odd. Could i then rightfully say that i have states 7 and 4 on an interval $-d/2<x<d/2$?
Aug
7
comment Wavefunction as a combination of two stationary states - how to find those states?
Can you add the equations you wrote in terms of integrals so i can understand more. Please allso leave the Dirac notation.
Aug
7
comment Wavefunction as a combination of two stationary states - how to find those states?
What would the states be if i had for example $\psi=\begin{align} A\left[ \cos \left(\frac{7 \pi x}{d}\right) + \frac{1}{3}\sin \left(\frac{4 \pi x}{d}\right)\right] \end{align}$? I put the cosinus inside instead of sinus.
Aug
6
comment Wavefunction as a combination of two stationary states - how to find those states?
Are you sure that the book is wrong? I need to be sure.
Aug
6
revised Wavefunction as a combination of two stationary states - how to find those states?
added 2 characters in body
Aug
6
comment Wavefunction as a combination of two stationary states - how to find those states?
Woops it is an infinite well - I fixed it.
Aug
6
asked Wavefunction as a combination of two stationary states - how to find those states?
Aug
6
comment Finite potential well problem - calculating the ground state
Wouldnt i get the energy of this state if i used hamiltonian on the wavefunction???