Position and Momentum Operators in Quantum Mechanics

We've learned a bit about quantum mechanics from a strictly conceptual and qualitative standpoint. But now it's time to dig a little deeper. Quantum mechanics is mathematics, so if we want to understand it on a fundamental level, we have to dig into the math. Unfortunately, the math is rather complex, so a solid understanding of linear algebra and differential equations is assumed here. But luckily, I have covered all of these topics in my mathematics playlist, so if you are committed to understanding quantum mechanics but don't have the math background, just head over there first to get the math down, and then this stuff will make sense! In this video, we start out by learning about operators, what they are and how to use them, the position and momentum operators, and how to apply them to the wavefunction. Don't be scared, it's fun!

Script by Hèctor Mas

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[adamdrewko]

Wow, I'm just so glad you're doing more than just a conceptual course on quantum mechanics and as always your video's crystal clear and high quality. Thank you so much for what you do for all of us learners and I'm waiting for more.

[adahaholu]

Yay, another video I won't understand but watch anyway.

[nono]

Now I appreciate the 3 semesters of electrical engineering that taught me the mathematical language needed to be able to patially follow this at two in the morning instead of going to sleep so that I could be productive in the low skill job I have to attend at 8 in order to pay my bills.

Your videos have the perfect pace and are super clear and on point. Well done.

[xonikkiecal]

I am so happy you posted this. As a physics major there’s only so much conceptual videos will do for me. I can read the textbook multiple times but math needs to be applied (duh). Once you get to higher mathematics and higher level physics, professors don’t bother with showing examples anymore so we have to just figure it out like a physicist should do. So think god for these advanced mathematics videos for modern physics!!

[MegaXRadioMan]

Amazing work! In my years working in physics, I've never encountered such a clear explanation of quantum mechanics with this level of mathematical rigor. This is an excellent stepping stone for a curious general audience.

[CandidDate]

The way he clearly and concisely massages the formulas really stimulates my math senses.

[watchdatclip]

Thank you so much Professor Dave! I was searching for Youtube videos that explained the mathematical side of quantum mechanics and your videos are honestly the only one I found, and the best too! The way you explain these are so articulate and perfect for anyone to grab the idea. Thank you again so much! Subscribed! <3

[cguy]

Btw, at about 12:30, where you discuss the partial time derivative of Psi, your explanation was perfect, but I have found that some confusion can be cleared up by first rewriting e^i(kx-wt) as e^ikx * e^-iwt. Then, it is quite easy to see that e^ikx is a constant, call it C, so you are taking the partial time derivative of C e^-iwt, which of course is -iw Ce^-iwt, which is just -iw Psi.

[davidhigham]

I learned more in one hour of taking notes, pausing, and doing the math at my pace with this video than I have in 8 weeks of struggling to keep up in my university course. I may just pass my midterm at the end of this week. Thank you!

[Yatukih_]

A truly enjoyable video to watch. Professor Dave feels at home when describing the concept of anything highly complex with regard to math and physics . He may find it a bit funny, but math fascinates me as well. Every day I read chapters from an over 1000 page thick Princeton companion to Mathematics, with the intent to just calm the mind and be more logical during the rest of the day. Momentum operators in quantum mechanics are indeed welcome and further research is required to decipher their remaining mysteries. Thanks for this!!

[LunaticBiker]

Never delete these videos, i'll be back next year

[KK-rgnj]

I'm so glad I found this video. This is such an amazingly exhaustive work explaining operators. My physics class is running ahead of my math class so I have to watch youtube to bridge the gap. Thank you soo much for this video!!!!

[matiassantacruz]

These videos are a godsend. I am a second year student in university, and even though our professor is pretty good, the flow of lectures and of most textbooks introduce far too many concepts at once do not explain the rationale for creating them. Thanks so much Professor Dave!

[aleksanderkardyka]

It just boggles my mind how scientifically sophisticated this man is! Kudos to you, Mr Farina! ^^

[OwenMcKinley]

Haven't even watched, and I already know this is going to rock. Thank you, Professor Dave.

[rholin]

I absolutely love how you introduce this material, and I agree, there really is no way to understand this material without the math.

[josesaldivar]

Very cool , crystal clear.
You know, while starting my grad studies, I wanted to film videos of each class as O had recorded audios on mini tape.
I was dreaming on a computer based system. The internet days were at using menus or **** and a year later Netscape appeared.
Now it is so good to have these accurate well pronounced lessons on demand, thanks to professors like Dave.
Many thanks, and It should be in each And every lesson.

[MiltonRosso]

I am so glad you're doing this, I have been wanting to learn about the math of quantum mechanics for a long time.

[thatomokoena]

I'm no physics student but I love your videos and try to learn what I can. Thank you for your work Prof

[qxzgdep]

I really do love this math stuff. I'm telling you there are no videos talking about math of this depth