\braket{x|p} = ? Inner product of position and momentum eigenstates

Hey How to Basic here to show you what the inner product of these two eigenstates are. plot twist it's not zero in case you thought it be zero.

[PrettyMuchPhysics]

In order to remember whether <x|p> has the plus or minus in the exponential, think of a video game where you collect experience points (xp) -- their value only goes up, therefore <x|p> has the plus sign and its conjugate <p|x> has the minus sign :D

[toodlewoodle]

You don't know how much you have influenced and inspired me to dream of a career in Physics!The videos on how you study for your Finals or how to be good at Math, the books on classical mech, Quantum mech and Math methods you told in your videos and gave the pdf link in the description-I have downloaded all of them and am trying to get through them(btw I am in the 12th grade).I love them a lot!Very helpful, especially the Griffith's Electrodynamics, John R.Taylor's Classical Mechanics.I have started with Shankar's Principal of Quantum Mechanics and the book on Quarks and Leptons.Just like you, I am a FAN of Quantum theory and stuff and dream to be a Quantum Physicist someday(that's exaggeration, I know).Your psychology towards Studying Physics and Math have encouraged me to think the same way you do.I want to lead a life just like you.Just wanted to say a BIG THANK YOU to you for influencing my life and changing it from a sluggish, monotonous, shitty one to a life full of Potential energy and encouraging me to convert it to the kinetic one.Wish I could meet you some day after I have built my dream carrier!
One thing I forgot to mention!Never Stop making this awesome useful videos!I don't want to lose contact with such a mind boggling Physicist in this HUGE world.Keep up this great job!Greetings!Can you make an educational series on Quantum Physics for noobs?That would be a great help!

[ImmProxy]

Just stumbled onto your channel and I can confidently say don't understand most of it (ive only taken up to calc2 so far) but you're super funny and very entertaining :)

[somecreeep]

So glad I found this video 6 months after I needed it.

[mattias]

Love your videos, youre such a good resource for someone like me who wants to go into phhsics. You present us with the real life of a physics student, and I myself take it as a good sign that i dont get bored or scared by your videos but rather i bevome more intrigued by the field.
Keep doing what you do.

[Myxinidae]

This was exactly what I needed when I needed it. Thank you.

[jaclynrebstock]

watching this before my graduate quantum final. THANK YOU

[elijahsmith]

Thanks for the video. It was nice to know the significance isn't obvious. It wasn't to me anyway.

[qubeat]

I just put this in a playlist so that I don't forget where to find this video when i'll inevitably forget where the expression comes from again

[simplyframes]

Cool video, very understandable. just one thing, What did < phi | X^ | psi> mean? Is it the value of the operator when the system goes from state psi to phi?
Thanks

[klassjostedt]

Kazoo kid is always a welcome sight, though a bit unexpected here! :'D

[blackcow]

amazing video i like it so much thx from north korea

[stevenlin]

There is a more straightforward proof by rewriting the quantum state in terms of position(or momentum) coordinates by inner products formula. And then rewrite the quantum state in the inner product as momentum(or position) specification, and finally compare to the Fourier transform formula to get the result. The proof is much simpler.

[physicsguy]

You've assumed the answer in the Fourier transform that you've boxed, and one can show that in one line! Take "Psi" to be a momentum eigenstate itself with momentum "p". Its wave functions in the position and momentum basis are, by definition, Psi(x) = <x|p> and Psi(p') = delta(p' - p). Plug these into the first Fourier relation you've assumed:

<x|p> = 1/sqrt(2pi) * integral delta(p' - p) e^(ip'x) dp' = 1/sqrt(2pi) * e^(ipx)

And there you go.

[rakingilani]

you threatened those states with a hermitian dagger at the start lmao

[kennbeary]

Omg I always saw those in my stats class but didn't really know what they were and now I know! :D

[brandonberisford]

you have no fucking idea how relevant this video was too me for my quantum mechanics final. I actually understood this, except there's one thing I don't understand. I have a very poor background in fourier theory. Could you possibly make a video explaining why psi(x) and phi(p) = those integrals and how you can derive them without Fourier transforms unless that's the only way???

[ztac_dex]

Thank you for this since Sakurai won't tell me nicely how to do this

[Hkj]

Why did you apply delta function twice (1st on |x'> and 2nd time on x' ) when you wrote |x'>x' delta(x'-x)

[ZelForShort]

I dont know any of this yet but for starters....square matrix? Completeness? Coord vs Work space?