Lecture 3 | The Theoretical Minimum

January 23, 2012 - In this course, world renowned physicist, Leonard Susskind, dives into the fundamentals of classical mechanics and quantum physics. He discovers the link between the two branches of physics and ultimately shows how quantum mechanics grew out of the classical structure. In this lecture, he works through some of the mathematics behind vectors and operators as used in physics.
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[Lucas-ssxi]

Lecture 3 - The Principles of Quantum Mechanics
00:00:26 - 1.9.5 Orthonormal Bases ("Better vector notation")
00:08:06 - 3.1 Mathematical Interlude: Linear Operators
00:09:06 - 3.1.1 Machines and Matrices
00:24:50 - [<A|M]|B>=<A|[M|B>]
00:30:35 - 3.1.3 Hermitian Conjugation (<A|M†=<B|)
00:42:30 - 3.1.4 Hermitian Operators (M†=M)
00:46:10 - 3.1.2 Eigenvalues and Eigenvectors
00:51:40 - 3.1.5 Hermitian Operators and Orthonormal Bases
01:01:21 - 3.2 The Principles of Quantum Mechanics
01:20:42 - 3.4 Constructing Spin Operators

the names of these chapters are taken from the following book:
Leonard Susskind, Art Friedman - Quantum Mechanics: The Theoretical Minimum (2014)

[雪奈-kt]

"The only way that somebody like me knows so quickly what you are thinking, is having made the same mistake of course." A humble and wonderful teacher. Thank you very much for the easy-to-follow lectures. I wish I could become a nice teacher like you.

[elouv]

Lectures from world known professors are the best thing on youtube!

[clearz]

This is about my 5th attempt at getting through lecture 3 and I finally "get it". Now for lecture 4 yey :-)

[wouldhaves]

The relief that hits when he actually starts relating the math to QM :')

[uquantum]

Watching this lecture for the second time, found its abstraction difficult to get my head around the first time. Dr. Susskind is a deeply wonderful teacher and also has a kind voice that I like hearing, I just hit replay refocus, and finally it’s making more sense

[iExamineLife]

many thanks for making this free for all!! :)

[tianmingguo]

Amazing lecture series. I love how he derived Mij dagger, brilliant!

[jeffreylanz]

"you're probably saturated, but I'm not, so we're gonna continue. I'm on a high."

[jithunniks]

24:32, the reason it was called anti linear was because the process of complex conjugation was deeply related to anti particles. Wow...

[John-xxlw]

How does this only have 47 comments?? I can’t believe more people don’t find this interesting. It’s like existing in Harry Potter movies and not caring about magic.

[kevinldonnelly]

Pauli matrices describe Quaternions.
Quaternions(1843) are used for more accurate and faster 3D rotations in computer graphics.
The mathematics of electron spin and classical rotations is therefore the same.

[matrixate]

While this is very succint, it is very watered down and assumes you've had experience with formal Dirac Notation. This is good as a review but defintely not for a beginner because there are too many questions that don't get answered. Fortunately, other videos servce that pupose and then coming back to this lecture, it all makes way more sense.

[patriciaheil]

"The sum of the squares of the components of <a|a> equals 1" -- is that the same as saying that A has a 100% chance of taking on an observable value?

[brunoprates]

One question: The eigenvalues +1 and -1 for sigmaz are the values that appeared in the apparatus when we measured the spin. But the fact that the apparatus showed +1 and -1 seems completely arbitrary - it could have been built in a way that it displayed 57 when measured in the up direction and -33 on the down direction - or it could show an image of a turtle when measured in the up direction, and the image of santa claus on the down direction. I assume it doesn't make sense to say that santa claus woule be the eigenvalue in this case... so what really is the meaning of this -1 and +1? How are they not completely arbitrary?

Ps: loving the lectures!! Im watching them while I read the book, and they really compliment each other.

[girigupta]

How to decide the direction for solving the right and left because if you consider another direction then the answer comes out as in and out ? is there a convension ?

[AkamiChannel]

It was never answered why the expectation value for the electron spin is cos theta rather than the square of that.

[HughesMath]

My god so basic and slowly builds into complex.

[kspangsege]

@1:18:00 "I'm on a high" :-)

[davidwilkie]

Theoretical Minimum, self-defining instantaneous roots 1-0 probability dominant axial-tangential orthogonality, ONE Origin @.dt zero-infinity, aka Holographic Singularity hyperfluid Space-time, pure-math relative motion positioning tangency containment, here-now-forever.

Of course the Nomenclature means what it says, it was defined to do that, and so it's required by Students to say if the results in applications are meaningful to them and either carry the applications forward or ask how. This is a typical Teaching and Learning reiteration of "judgement of Act-uality" in Completeness.., in Correspondence with e-Pi-i-numberness Quantum-fields resonant shape shifting Calculus and Superposition-point Number Relationships.

Because "Everything is Theoretical" ie pure-math relative-timing rates integrating Fast and Slow orientation of perceived Reality in Real-time Actuality, (aka Math-Physics), the re-evolution circularity quantization cause-effect that is Calculus of Time Duration Timing Conception, Singularity zero-infinity sync-duration is Eternity-now quantization here-now-forever. Circularity logic, or Observable Logarithmic Time.

And of course, resonance reality floating in theoretic No-thing confined Noe in/of e-Pi-i-reflection logarithmic condensation positioning, makes it difficult to look at ONE-INFINITY Singularity Eternity-now Interval as anything other than hyperfluid "vapourware". If you don't have a lead-in recognition, learning by doing, then you're stuck with a recital of memory associations like "poetic naturalness".., which is derived from actual e-Pi-i sync-duration connectivity, all-ways all-at-once instantaneous realization, ..literally reading self-defining Actuality. Which only involves "changing your mind" and re-labelling the perceptions, not the lecture, because the pure-math relative-timing rates, collapsed quantization holographic picture demonstrated, remains the same.

Holographic inside-outside e-Pi-i sync-duration resonances Modulation is The Calculus.., obviously, once you get it in Superspin-spiral Superposition-point Singularity Positioning. Otherwise, it's back to basics, ..meditation on No-thing, from the koan "where was I before being...?", to WYSIWYG here-now-forever continuous creation cause-effect connection = Singularity. Daily revision of experience.