Lecture 7: More on Energy Eigenstates 

I took 3 semesters of graduate level mathematical quantum physics, so I already understand the mathematics a lot better than it is presented here, but the amount of physical insight provided in this lecture series is amazing.

Last year, I took Quantum Physics courses at my university. Now, by watching these videos, I am understanding what they passionlessly tried to explain in those courses. Thanks! :D

The quick questions part is most amazing. It shows how difficult it is to really understand the subject. Great work.

He gets an applause in every lecture! Just amazing!

At 14:31, where the subtitles says:[INAUDIBLE], I think the guy in the audience said: "do we ever find discretization for position". And thank you for uploading such amazing lectures!

This instructor is so good, just amazing.

It’s refreshing to see such passion

it all makes sense now! I always thought my professors were crazy trying to explain this to us.

The ending is better than that of an episode of Breaking Bad!!

The solution to the SE near the end of the class (~1:04:00) is quite intuitive and inspiring.

Man I wish I would’ve watched these videos when I took my physical chemistry coursework lol 😂 it all makes sense now! I always thought my professors were crazy trying to explain this to us.

the last 15 mins of the graph about allowed region and forbidden region saved my life. my prof never analyze the formula and derive the graph. allan adams is amazing.

Perfect title. When I watch this I truly feel like a More on.

Beauty of physics to discribes unknown things . ♥️♥️♥️

The really blew my mind at the end, I was like woah dude.

Incredible lecture!!! THANK YOU!!!!!

Can I add my own "thank you AV person" ... clear crisp audio, clear crisp video... nice.

A really nice set of lectures. I am up to #7 so far. I am not sure all the lecture notes will be available though. They use three reference books for the class. Must cost the MIT students a fortune!

Incredibly insightful

@1:10:38 Why does the wave function not equal to 0 at the turning point? And why it must be continue at boundary of the allowed region? What does he want to say at all at last 5mins lecture?

Inspiring :) Thanx for sharing knowledge and make it accessible for everyone around the world :)

Hey MIT, any chance of posting the rest of the lecture notes? The site provides just the first eight... Thanks anyway for the great initiative!!

How do I show equation 1 by explicit calculation?

HEART BEAT FROM WHERE RESUSCIATION IS POSSIBLE

The site provides just the first eight... Thanks anyway for the great initiative!!

thank u amazing lectures

I watched this after a touch of dinner liqueur and I finally understand quantum physics! I better enjoy it while it lasts.

... It would be cool if we had informations about analycity on wave function. He autorizes nonzero functions with a finite support in this video (twice), but on a previous one he explains that translations are exponential of differentiation, admitting the analicity of wave functions... (sorry for my english :3)

In Allan Adams we trust.

At 56:34 there shouldn't be a square root for (2/a). Anyone please confirm this.

Great lecture

watching that final analysis was wild

Lebesgue integral takes care of both discrete sums (with discrete measure) and "continuous sums".

是不是由于能量是一个标量，并且这个标量不随时间而变化。因此波函数的能量形式才能有包含时间的简单形式。（17：34）

The statement at 1:10:23 doesn't seem to be true. The amplitude is captured at the constant A and B in the solution, and they are not k dependent, i.e. do not change with the difference between U and E

at 17:06 he says solutions of the shrondinger equations add to become solutions of the schrondinger equation what does it mean?

Wonderful content. Much appreciated. Just a minor technicallity: (phi)" should not be read phi prime prime, but phi second [derivative]. And of course superscripts this kind may proceed with third ('''), fourth, fifth, etc., in small italic Romans, wherein prime means 'the first.' Useful for derivative functions, but also for any other numerable, sorted stuff. For instance, time divisions: hours (h), [prime] minute [hour]s ('), second [minute hour]s ("), and angular units: degrees (º), [prime] minute [degree]s ('), second [minute degree]s ("), whose extended forms have almost fallen into oblivion, and only their abbreviated ones remain in use.

At 43:05 where the subtitles say, "[INAUDIBLE]", I think he is saying, "Frequencies are like energies *modulo on* h-bar".

Pretty good teacher

@23:12 why at position L "the fact that this goes to 0"?? @25:20 when n=10000, then there're 10000 point in 0~L where particle couldn't appear because the probability of these point = 0. Is that possible??

thanks MIT ....this dude is awesome......free mind candy 4 all....1 way 2 help fix the future 4 sure ! .....only hundreds of views wtf !?.....prob shoulda had piano kitty teaching instead...jeez

This course is a million times easier to understand after taking graduate linear algebra

In case of electron around hydrogen nuclei values of momentum are also discrete. Why don't we use the sum symbol for k, like we use it for energy?

This vid series is a wonderful supplement to my textbook (Griffiths). While Griffiths lays out proofs relatively clearly he seems to side step a lot of the physical meaning of the equations. And though the appendix gives a refresher on linear algebra, I find that it too fails to attach the math to physical meaning. Its really easy to get very deep into methods for solving systems while forgetting the physical interpretation of the methods and solutions. This vid series corrects that.

Why does he write the dx before the integrand? Sorry if this is a stupid question - I'm a high schooler that only knows basic calculus

Also, I'm taking DE right now and we're talking about eigenvalues and eigenvectors with matricies. What does "eigen" mean? It seems that the name is all over the place

The question at 37.00 - shouldn't have answer C since we just know the coefficients & not the eigenfunctions, isn't it?

At 45:33 i think that the [INAUDIBLE] part says:" frequency but then you have that group velocity is still time dependent".

Can someone help me out about the question at 49:25 ish, i thought when width of well goes large in number wave function became something has more waves which mean higher frequency and it leads to higher energy, but i know k equal 1 over L and k and energy are proportional but i dont know why i had the feeling of what i wrote first.

The reasoning at the end seemingly leading to nothing and then all of a sudden the aha that's why discrete Energies was beautiful lol

I find it so hard to accept that electrons are binary like that . It has to be the scale like day and night isnt binary but at a relative scale it would sure look at way . But anyway ,why do blood cells stick together exposed to non ionizing and conversely separate when grounded . They are acting like their missing electrons and when in contact with the earth they return. Is there an energetic state that you can force an electron into , not by observation and wave collapse. But with emf , non ionizing excitation of valance electrons ?

curious about what professor drinks using that bottle, coffee?

2:00 !!!!!! 7:00 degenerate eigenfunctions + linear combinations of them 25:30 33:00 they’re incompatible & do not commute. 43:00 53:00

Adams must have known his position since he kept speaking so fast.

Just wanna be a MIT student...

6:29 who is Shri Kulkarni and why is “phi star” in honour of him? (Sorry I’m sure it’s a hilarious joke that explanation detracts from!)

great great great

first... also what did he mean by "morally equivalent" at 2:05???

@2:41 why does he thank the AV person?

Is there an infinite state of infinite states ??

At about 42 minutes, he forgot to take integral when computing the probability. Second, the answer should be "Yes, always" because we are talking about eigenstates and eigenstates are always orthogonal on each other.

why energy is not be in a integral form of superposition ?

I wish I was there in that class......

36:27 Why B please?

Yeah but for me its like super symmetry.... cool so were there already

And three disliked this? :/

Professor Adams is just Awesome Sauce! 🤣💦

This one is a little bit hard

5:25 What???!

👍🙏

"Everyone cool with that?" Errrr..Sure.

[INAUDIBLE]

Anybody from India who called them Baingan values?

cool?

add

Smartest people in the world can't get the chalkboard to work...wait for the janitor. Doubt if any one in the room could change their own oil.

Lol I am just here to mind fuck myself. This is insane!!!!!

Mind-tools: Correlate the Intuitive Equivalence of the Black-body chalkboard and Temporal Singularity projection-drawing positioning in Eternity-now, as hyper-hypo temporal vector fluidity-> Superspin Polar-Cartesian coordination Calculus.., wave-package localization as density-intensity Vector-values, ..and the lecture has to "make sense", or no matter how long we look at it, we do not see and perceive the circumstances. (Speaking from experience) Something in Nothing is probability ONE Origin of omnidirectional-dimensional logarithmic interference probabilities in self-defining potential possibilities, of real-time significance.., ie Vector spaces. Eg Anti de Sitter space is the same context/concept of instantaneous real-time e-Pi axial-tangential sync-duration in i-reflection=> Containment (Eigenvalues) in the Universal standing wave-packaging of mass-energy-momentum, or Superspin-spiral embedded Modulation proportioning-positioning. This takes practice, all-ways starting with AM-FM Communication in real-time pictures of Temporal Superposition-point Positioning Singularity Conception. Childhood development experience is critical to Intuitive capabilities, that is nature, and mnemonic memory associations/techniques are nurture, often self managed. ----- The story goes that anyone who defends themselves in a Court of Law, (law-based on pure-math empirical laws of shape shifting temporal Calculus), "has a fool for a Client", which might be why Feynman said the easiest person to fool is yourself when deriving physical theories. The laws of Mathematical relative-timing ratio-rates in terms of AM-FM e-Pi-i sync-duration resonances are derived from logarithmic Inflation, Condensation FM raised to natural log/antilog powers into the Eternity-now density-intensity numberness Interval Conception of reference-framing Holographic Principle Imagery of perceived Reality. This is the inside-outside Superposition-point Singularity Superspin Modulation Mechanism by which we make Theoretical Judgements about abstract reasoning components of perceived Reality. When Reality teaches us, this is Actual Intelligence, when we project accumulated Intuitions such a Euler's e-Pi-i Mathematical Conjectures, (confined to 2-ness duality.., i-reflection picture-plane containment, theoretically => 3D-T), we are compelled to assume the continuous creation connection cause-effect context of ONE-INFINITY Singularity.., the Universal pivotal concept of vanishing point-zero-infinity Black-body containment. Under the circumstances, BBT is non-sense because of the implied discontinuity of a zero Time beginning, when the actual Centre of Time Duration Timing, or here-now-forever, is self-defining zero-infinity sync-duration, e-Pi-i connectivity. Disproof Methodology is always apparent in the Observable Eternity-now Actuality Reality, logarithmic quantization Interval. Review, reorientate and reiterate from/by First Principle Observation.., relies on a beginng teaching observable manifestation of Actual Intelligence inherent in Actuality. Eg Ancient Greek (revision) for Geometry, Conics and point-line-circle drawn alignments from observed Celestial time-timing phenomena. Followed by Euler's e-Pi-i Mathematical assembly of what constitutes a Disproof Methodology.., elimination of disconnect to reveal universal Centre of Time Duration Timing e-Inflation potential +/-, Pi-bifurcation radiance and i-reflection containment in vanishing point-zero-infinity Black-body Singularity reflection of/by No-thing-defined eternally, equivalent to instantaneous trancendental expansion-condensation .dt omnidirectional-dimensional cause-effect self-defining Origin.

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Why did physicist insist so much on bracket notation? So annoying from a math person perspective.

morally equivalent to a dot product? 🤣🤣🤣🤣🤣

Consciousness is all there is. See my paper "How Self-Reference Builds the World", author Cosmin Visan*

I know a 16 year old shouldn't be watching this playlist but I just wanna say, he talks way too fast, especially when i don't understand the topic or equation.

He is so slow, I watch it on x2 speed and its still not fast enough I want x10 speed

I understand u

We r at war

But… they don’t

Your not speaking english

cool?