Lecture 4 | The Theoretical Minimum

January 30, 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 continues his discussion on the vectors and operators that define the language of quantum physics.

Stanford University:

Stanford Continuing Studies:

Stanford University Channel on YouTube:

[smajidy]

0:00:00 to 0:23:09 - Review of postulates
0:23:10 to 0:56:40 - Evolutions in time
0:56:41 to 1:11:55 - Expectation value
1:11:56 to 1:37:34 - Time evolution of expectation values
1:37:35 to 1:47:22 - Conservation of average energy

[Lucas-ssxi]

Lecture 4 - Time and Change
0:00:00 - Review of 3.2 The Principles
0:23:10 - 4.1 A Classical Reminder & 4.3 Determinism in Quantum Mechanics
0:26:45 - 4.2 Unitarity
0:30:48 - 4.4 A Closer Look at U(t): (U(t)†U(t)=I)
0:39:07 - 4.5 The Hamiltonian
0:49:31 - Generalized time dependent Schrödinger Equation
0:56:43 - 4.7 Expectation Values (Average Values)
1:11:56 - 4.9 Connections to Classical Mechanics
1:37:35 - 4.10 Conservation of Energy

1:26:40 to 1:30:00 - 4.6 What Ever Happened to ħ?

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

[andrewcriscione]

These will be viewed as the modern Feynman Lectures, thanks Stanford!

[rshxrma]

I'M DONE. I'm really jealous of him eating those sweet delicious-looking whatever those are!

[stevejones]

44:00, he keeps dropping these bombshells! Hamiltonian and energy are the same. Before he said that 'normal to' and 'orthogonal' are the same.

[capitanmission]

2nd law of thermodynamics correctly restated by Lenny: Entropy probably never decrease :D

[johnboro]

I have absolutely no idea what he’s talking about, but I know it’s in English. It’s fascinating listening to you someone so clever, the best way I’ve found to sleep ever, I love it

[-nc]

If you have two orthogonal vectors corresponding to the same eigenvalue, say 1, how could you possibly distinguish between those two states? The only measurement you’ll see is “1”! But you’re supposed to be able to distinguish between orthogonal vectors?

[danfara]

Thus, is the misterious "i" in Schröndinger equation being explained by saying
U=I+a H with H hermitian and U unitary and "a" a complex number necessarily "a" has to be purely imaginary?

[TheVivek]

1:23:49 Learning a bit of french certainly helped there

[enisten]

Can someone explain why the probability of observing a degenerate eigenvalue is the same regardless of which set of orthogonal eigenvectors we choose to use? Depending on this choice, we will get a different set of inner products with the state vector. So, how come the total probability of observing that degenerate eigenvalue remains unchanged?

PS. I understand it must be invariant because the sum of the probabilities of remaining eigenvalues doesn't change. But I'm looking for a direct and intuitive explanation.

[chimaru]

For his explanation of orthogonal space vectors, if you are "prepared" with an "up" or "right" and measure along the z axis and measure "-1" wouldn't that tell you that it can't be up and thus has to be left?

[jeffreylanz]

8:35 haha looks like a child's drawing of a dinosaur

[guitar_jero]

Wouldn't it be better if we defined the Poisson brackets as:
{A, B} = lim h->0 (2πi/h)*[B, A] ???
So, it's a 0/0 limit and therefore the left side can exist and be unique.

[gershunistepan]

Entropy never deacreases except when it does xD

[Gwunderi]

"It's pure pluginology" he sais at min. 1:09:25 - so nothing simpler than QM maths : )))

[zphuo]

@26:00 Although QM is full of randomness, it is still reversibility & Information conservation. Why?
@52:00 Generalized time dependent Schrodiger Equation.

[xinzeng-iqzv]

conditional probablities for beginners

[raghavendrakaushik]

At 14:47 shouldn't the probability be <A|Lambda><Lambda|A> as discussed in the previous lectures? It is not just square, it is square of length of the component.

[addis]

@21.47 he is crying for oreo or quantum entaligment?