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Aug
15
comment The probability of finding the electron in the H-atom
I know if i want to get the full probability i need to calculate: $$P=\int\limits_{V}|R(r)|^2|\Phi(\phi)|^2|\Theta(\theta)|^2dV = \int\limits_{V}|R(r)|^2|\Phi(\phi)|^2|\Theta(\theta)|^2\,\,r^2dr\, d\theta \sin\theta d\phi=\\ =\int\limits_{0}^{\infty}r^2|R(r)|^2dr \int\limits_{0}^{\pi}|\Theta(\theta)|^2 \sin\theta d\theta \int\limits_{0}^{2\pi}d\phi$$ I hope i wrote that right and i think that this full integral should equal 1. But somehow it is still not clear to me how to get the $P(r)dr$... How can i interpret the $dr$ after the $P(r)$. What do you think of when you see something like it?
Aug
15
comment The probability of finding the electron in the H-atom
How do i do this?
Aug
15
comment The probability of finding the electron in the H-atom
Never mind i think i understand :)
Aug
15
comment The probability of finding the electron in the H-atom
I have one more question about this. Why did we use the diferential of volume when we are searching for $P(r)dr$
Aug
15
accepted The probability of finding the electron in the H-atom
Aug
15
comment The probability of finding the electron in the H-atom
Thank you very much. So if we are satisfied with a fraction of a probability there is no need to integrate :) What confused me was that feeling that if we want to integrate the equation we have to do it on both sides and not only one side... It is weird to me that we integrate just part of the equation.
Aug
15
asked The probability of finding the electron in the H-atom
Aug
8
asked Quantum tunelling problem - got a weird imaginary ratio in the end
Aug
7
comment Moving electron - finding the wavefunction
Thank you very much for the extended anwser. Now i do understand.
Aug
7
accepted Moving electron - finding the wavefunction
Aug
7
comment Moving electron - finding the wavefunction
Well the Lorentz invariance is a fundamantal equation of relativity and it says that $E=E_0$. If i then use $E=E_k$ to calculate constant $L$ it seems to me that i have violated the special relativity and everything Einstein wrote...
Aug
7
comment Moving electron - finding the wavefunction
I do not understand...
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