Density of States - Statistical Physics - University Physics

[@dbf72829]

One day this is gonna be the most watched video on yt on statistical mechanics

[@Jake-fk5zw]

Thank you so much for taking your time when covering this.

[@CanErtugay]

Thanks for the really clear explanations, but you wrote k=2 pi n/L, I think it must be pi n/L ?

[@honorcolling5556]

Saving me yet again, this is such a good video thankyou for putting so much time into it

[@yagmurerhan8132]

hey thanks a lot for these videos! shouldn't the quantization condition be k*L= pi*L instead of 2pi?

[@spacedee6968]

Just wow, thanks for making this!

[@xgozulx]

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

[@pazzy768]

Thanks! Yea you can swap things out for different dimensionalities and different dispersion relations!

[@dbf72829]

@@pazzy768 Mr pazzy what book do you follow for statistical mechanics?

[@MathEnth-rz3tt]

22:00 isnt k=npi/L?

[@Rafid_Ahmed101]

same confusion.... T_T

[@blackhole1222]

vey useful, thanks!

[@John-bq1lp]

good video!

[@nwxxzchen3105]

where does the formula E=(h^2n^2pi^2)/(2mL^2) come from?

[@TryhardGenos]

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?

[@CHEPhysics]

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.

[@CHEPhysics]

The Mandl textbook does a good job of explaining this concept.

[@CanErtugay]

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... ???

[@pazzy768]

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!

[@dbf72829]

Please upload more videos on statistical mechanics

[@omega-55555]

Stat mech video en route ;)

[@melanogaster4586]

tnq so much

[@dbf72829]

Waiting on your new video's on stat mech

[@omega-55555]

A few more messages and I reckon we will get one

[@dbf72829]

​@@omega-55555haha mate we got ig

[@dbf72829]

I'm waiting

[@dbf72829]

I'm waiting Mr praxxy We want stat mech We want stat mech

[@omega-55555]

We want stat mech we want stat mech

[@paladin1147]

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]

What conditions are you referring to exactly?

[@paladin1147]

@@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

[@paladin1147]

@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