1. Bras, Kets And Operators | Weinberg’s Lectures on Quantum Mechanics

#quantummechanics #StevenWeinberg
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬

0:00 - Introduction
4:45 - Dirac’s Bras & Kets
8:04 - Matrix rep. - State vectors
8:59 - Ket is linear, Bra is anti-linear
10:09 - Meaning of State vectors
13:05 - Probabilities
16:13 - Normalisation of States
18:20 - Hilbert space
19:44 - Operators
20:48 - Identity Operator
21:51 - Projector, Ket-bra
22:50 - Expectation value of Operators
23:26 - Projectors into Sub-spaces
24:20 - Properties of Projectors
25:54 - Hermitian Conjugation of Operators
26:52 - Hermitian Operators
27:28 - Observables are Hermitian Operators
29:31 - Functions of Hermitian Operators
31:33 - Operators as Ket-bras
33:17 - Matrix rep. - Operators
35:31 - Matrix rep. - Hermitian Conjugation
36:39 - Hermitian Conjugation - Examples
38:47 - Operators - Eigenvectors, Eigenvalues
39:41 - How to find Eigenvectors & Eigenvalues
46:41 - Hermitian Operators are Observables
48:59 - Theorem - Eigenvectors of Hermitian Operators form a Basis
56:35 - Commutators
58:14 - Commutators - Product rule
59:32 - Theorem - Commuting Hermitian Operators share Eigenbasis
1:05:18 - Complete description of Quantum systems
1:08:28 - Complete set of Commuting Operators
1:10:56 - Ending

This is lecture 1 of the series, where we discuss and explain the book, “Weinberg’s Lectures on Quantum Mechanics”.

This is (part 1 of) chapter 3 of the book.

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► Full course :

References :
► Inverse of a Matrix:
► Levi-Civita Symbol:
► Determinant - Leibniz Formula:

Some more good books for your physics reading list :
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►Susskind’s Theoretical Minimum series :
►Landau & Lifshitz series :
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[physicsdaemon]

Thanks for watching!
Leave your questions in the comments; so that I may answer them in a follow-up video.

[gokayakcay]

Finally found someone who explains step by step. These series are treasure, thank you so much!

[inevitableheatdeath]

I remember in my post graduation days I had very hard time while self studying this book and ended up with Landau Lifshitz. For me this book is next to Jackson's Electrodynamics, in terms of difficulty if you're self studying. I am looking forward to your lecture series and this first lecture gives me hope 🙂

[sengeeran]

excellent display with utmost clarity....thanks

[nc]

Such a fantastic way of explaining quantum mechanics and the mathematics that accompanies it!
It's is absolutely gripping!!

[rv]

The map ψ —> |ψ> is not _just_ linear: IT'S ACTUALLY THE IDENTITY MAP!
So writing |ψ> is completely useless, as you could just write ψ.

And then, when one writes
|λ> for an/the eigenstate of eigenvalue λ, the map
λ —> |λ> ceases to be the identity map and becomes the map associating to an eigenvalue its corresponding eigenvector (when it is unique...).

There's no wonder why many mathematicians rightfully cringe at the "bra-ket" notation!

[nc]

I tried to absorb as much as I could from this lecture.