this helped a lot, I also didn't really get the density of states calculation, yours is much clearer, in class what we did i think is maybe more general, but is such a mess
So we take into account all states, including ones which have n = -1,-2,-3 as they correspond to electrons moving in the opposite direction! These are also valid solutions to the standing wave equation!
hi, thanks for this amazing video. U really make me love physics way more than my uni xd. Could u please explain why for example electrons we have to multiply by 2 for the dos? I understand that they have 2 different spins so they have 2 states for 3 same quantum numbers.Dont we take those 2 different states into account while we measure the states when we count them with Σ..... and later with integral so we can find that way the dos?
I think the most intuitive way to understand this is to take the most general expression possible for the density of states and then multiply by 2 for the spin degeneracy. This is a general approach you can use for other situations as well. For example, take the most general expression for the density of states and then multiply by 2 in the case of EM waves to account for both possible polarizations.
Ama be real, your derivation doesn't always work for different conditions, or I am really stupid. I really like your derivation, it is super clean but it doesn't always work.
@pazzy768 Ayyy, I love your videos, tho I did pretty well on the test and was just sad that the way you derive it doesn't work sometimes, or I am doing something wrong
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Thank you so much for taking your time when covering this.
One day this is gonna be the most watched video on yt on statistical mechanics
Saving me yet again, this is such a good video thankyou for putting so much time into it
this helped a lot, I also didn't really get the density of states calculation, yours is much clearer, in class what we did i think is maybe more general, but is such a mess
Thanks! Yea you can swap things out for different dimensionalities and different dispersion relations!
@@pazzy768 Mr pazzy what book do you follow for statistical mechanics?
Thanks for the really clear explanations, but you wrote k=2 pi n/L, I think it must be pi n/L ?
Just wow, thanks for making this!
hey thanks a lot for these videos! shouldn't the quantization condition be k*L= pi*L instead of 2pi?
where does the formula E=(h^2n^2pi^2)/(2mL^2) come from?
good video!
vey useful, thanks!
please let me ask a question, The reason that we take into account only 1/8 of sphere is all the components of k equal npi/L, and n=1,2,3... ???
So we take into account all states, including ones which have n = -1,-2,-3 as they correspond to electrons moving in the opposite direction! These are also valid solutions to the standing wave equation!
22:00 isnt k=npi/L?
same confusion.... T_T
hi, thanks for this amazing video. U really make me love physics way more than my uni xd. Could u please explain why for example electrons we have to multiply by 2 for the dos? I understand that they have 2 different spins so they have 2 states for 3 same quantum numbers.Dont we take those 2 different states into account while we measure the states when we count them with Σ..... and later with integral so we can find that way the dos?
I think the most intuitive way to understand this is to take the most general expression possible for the density of states and then multiply by 2 for the spin degeneracy. This is a general approach you can use for other situations as well. For example, take the most general expression for the density of states and then multiply by 2 in the case of EM waves to account for both possible polarizations.
The Mandl textbook does a good job of explaining this concept.
Please upload more videos on statistical mechanics
Stat mech video en route ;)
tnq so much
I'm waiting Mr praxxy
We want stat mech
We want stat mech
We want stat mech we want stat mech
I'm waiting
Waiting on your new video's on stat mech
A few more messages and I reckon we will get one
@@omega-55555haha mate we got ig
Ama be real, your derivation doesn't always work for different conditions, or I am really stupid. I really like your derivation, it is super clean but it doesn't always work.
What conditions are you referring to exactly?
@@pazzy768 Like the prefactor doesn't come out right in 1D usually, it is missing 2 or 4 due to counting left and right states, sometimes in 2D
@pazzy768 Ayyy, I love your videos, tho I did pretty well on the test and was just sad that the way you derive it doesn't work sometimes, or I am doing something wrong