The physics of how to cool down your cup of coffee or tea fastest. Sponsored by Brilliant: https://brilliant.org/HiggsinoPhysics Stirring vs blowing vs cooli...
Oh right.. I think i misunderstood the question then.
I need to find ##< x(t)> ## for all later times.
But i can't see, how i can find that.. You are saying ##\frac{d<x>}{dt} \neq < x(t)> ##
I am not sure why i should fine ##< x >## I can see it's a part of the equation, but why does it give...
Oh I see. That's very smart.
This is what i did:
##\frac{d<x>}{dt} = \frac{i}{\hbar} <[H,x]>##
insert hamilton
##= \frac{i}{\hbar} <[P^2/2m,x]>##
##= \frac{i}{2 m \hbar } <[PP,x]>##
##= \frac{i}{2 m \hbar } <P[P,x]+[P,x]P>##
##= \frac{i}{2 m \hbar } <-P[x,P]-[x,P]P>##
##= \frac{i}{2 m \hbar }...
Actually when you say it like that..
I guess i thought in
## H = \frac{p^2}{2m} = \frac{\hbar}{2m}\frac{\partial^2}{\partial x^2}##
the ##p## is just a constant but off course it's an operator:
##p = i \hbar \frac{\partial}{\partial x}##
I guess the only thing to do is to differentiate a couple...
Hello physics forums. I'm trying to solve an old exam question. Would love your help.
Homework Statement
A free particle in one dimension is described by:
## H = \frac{p^2}{2m} = \frac{\hbar}{2m}\frac{\partial^2}{\partial x^2}##
at ##t = 0##
The wavefunction is described by:
## \Psi(x,0) =...
Okay i think i understand so we are calculating:
##\sigma_x \sigma_{L_x} \geq |\frac{1}{2i} <[x,L_x]>| ##
and not:
##\sigma_x \sigma_{L_z} \geq |\frac{1}{2i} <[x,L_z]>| ##?
Thank you for helping me.
Me and my group had a laugh at this, we are just finished doing it and it was very nasty indeed :D
Thank you very much for the comment.
- You mean ## <\sigma_{L_z}^2> ## and not ## <\sigma_{L_x}^2> ## Right?
We have actually calculated ##<L_z## and ##<L_z^2>## from another task. We did it...
Hi physics forms! I'm practicing to for an Quantum mechanics exam, and i have a problem.
1. Homework Statement
I have two problems, but it's all related to the same main task. I have a state for the Hydrogen:
## \Psi = \frac{1}{\sqrt{2}}(\psi_{100} + i \psi_{211})##
where ## \psi_{nlm}##...