Commutator: linear momentum and position

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00:08 Displacement operator in x direction (x) and linear momentum operator in x direction (pₓ)
01:04 Definition of commutator
01:45 Insert dummy operand
02:44 Apply nearest operator to function
04:08 Factor out constant
05:15 Apply product rule for differentiation
07:10 Remove dummy operand

Derivation of the commutator of the 1-D linear position and linear momentum operators.

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00:08 Displacement operator in x direction (x) and linear momentum operator in x direction (pₓ)
01:04 Definition of commutator
01:45 Insert dummy operand
02:44 Apply nearest operator to function
04:08 Factor out constant
05:15 Apply product rule for differentiation
07:10 Remove dummy operand

lseinjr

Introducing the dummy function was a neat technique, it really helped prove the relation in a more technical way that's not too complex nor too simplified.
Thank You

thesophisticatedtarzan

U made my day sir. Sometimes slow and clear explanation is what we need

uedlrgd

Thanks Dr. Sein I couldn’t figure this out

Jaybee

Thank you!! You explained this very clearly

ghostinthesnow

Now i get it, im gonna go to solve my homework- thank you, saved my life 👍

itsurshon

Thanks for the detailed procedure .great job.

Please solve more similar tricky problems

hemantj

Very helpful sir 🙏, thanks for clearing my concept

purpleworld

wow super helpful thank you very very much!

joyharrison

Awesome tutorial. Do you have for the commutator of position and Hamiltonian?

nicktumi

So if you switch the order of the operators in the communtator, it changes the sign of the answer?

LucianLusilver

Hi there, Isn't the momentum operator -i*hbar d/dx? i dont understand how -i becomes 1/i. Thankyoufor your time :)

AlexNewmantheNewMan

How do two matrices give a number ? Thank you for anyone who has an answer

lailadeen

How to cut the d (szi)/dx at last term?how it possible how sir?

swethakrishnaa

isn't the momentum operator -i h (bar) not i/h (bar)?

joshhazards

Isn't the answer ih? P_hat = -ihd/dx

taliam-o

this guy sounds like Chris from family guy

industrialdonut

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