One-Dimensional Box of electrons
What does this question even mean? How to approach this?
45 Replies
@Gyro Gearloose
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.I was wondering. Well, we can assume that since there are four electrons, they'll inhabit two energy levels, with two in each degenerate level (because spin)
Ah I see. Because of Pauli's exclusion principle right?
Mhm
Now, the ground state is that in which you have nodes on either end, antinode in the centre
I forgot the energy of standing waves, so I gotta revise, but that gives you E0
The second state will have a single node at the centre
Treat it like standing waves essentially
Okay, so the standing waves correspond to
Like how it would be in an organ pipe?
No, wait
String
This is string
Closed on both sides
Okay. Will try this with this approach.
physics que be like:
one dimension box
this is in Zumdahl too btw
It's a classic QM situation
oo damn
whats QM?
Quantum Mechanics
Yea this is intro to this topic
Before you do Schrödinger
Though there you'd use Schrödinger to find the unitary time evolution
@SirLancelotDuLac how much of this paper were u able to solve
Its not very tough, and yeah doable.
Some questions are a little tough but
Surely not allen aiots type stuff.
looks like i need to revise then lol
were u able to do ques 1
fluids+shm wala
That was dimensional analysis na?
Yeah.
oh lol i didnt read completely . i sensed fluids and ran away
will try again ig
Me in conics :sweaty:
lol same
@SirLancelotDuLac solved? Or should I send sol?
Please do, I'm still clueless ;_;
Just a moment
Heck , this is single correct
My handwriting is a mess
Ask if you don't get something
Also, technically it's the partial second derivative but we're in 1D, and not considering time evolution, so it's not important
sorry if it doesnt belong here but is there any youtube channel or smthing which will upload solutions to all three papers. prashant jain uploaded solns for maths
Not sure.
Can this be done without knowing schrodinger equation?
Okay, I get the gist of the solution...
But also how do we write the energy for the obtained wave?
Uhhh using standing waves I presume, but I have completely forgotten energy of standing waves so....
But that has terms of linear mass density and stuff.
Oh
Ah, but I get the solution now.
Can I send one more similar doubt in this thread?
Sure
Okay, I couldn't find the exact question, so take with a grain of salt, but the question was something like this:
We can consider matter to be a matter-wave that behaves similar to normal waves. Now consider an incline, with a matter wave going from A to D. One of the waves takes the path via C while the other via B. What is the phase difference between the two waves? (Dimensions of wedge are known)
You can just take path difference and multiply by 2πp/h right?
Path difference here should be zero here right?
Is the answer not zero?
Nope.
Wait Imma try to find the actual question tho...
Yes just use lambda=2L/n for standing wave condition then put that lambda in de broglie equation to get momentum and put that momentum in E=p^2/2m to get energy which yields same result i belive
I see. Momentum by h/lambda and mass of electron.
Yep that works.
+solved @Opt @integralofe^2x
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