this shows up in the derivation of the classical wave equation, also jensen's inequality is similar to this

isn't it "acceleration" when applied to time, isn't it "curvature" when applied to space?

Last video of Dhruv Rathee 😊

I recommend the people who are all beginners for quantum mechanics before watching the video try to read QCQI by Nielsen & Chuang. It might improve your understanding. Thanks for the series Sir.

my friend, why did you stop!

❤👏🏼👏🏼👏🏼

You need to go back and study basic calculus. You represented a finite range along the x-axis with a differential, dx, which is an infinitely small quantity. You should have used delta x, which has a finite value.I don't know what you studied in math but where I studied it, the meaning of the 2nd derivative was clearly explained. In fact, we went as far as the 4th derivative, much to our chagrin, since we were engineers and the prof was ego-tripping at our expense. If the first derivative of a curve is a straight line with a slope, what do you suppose the derivative of that straight line may be? Since the 1st derivative is the instantaneous rate of change of a tangent line to a curve, what do you suppose the instantaneous rate of change of that tangent line may be? The problem I found with Feyman was his smart-assed attitude. He once inferred to a group of student in a lecture in New Zealand that he could not explain his theory to them because they were too stupid to understand it. Feynman lived in a world of thought-experiments, much like Einstein, in which nothing could be observed or proved. How convenient? Of course, scientists claim to have verified their theories but those scientists were often groupies who were going long to get along.

Does it mean finding the rate of change of the derivative

Intro by home: went the like

Where the first derivative is a tangent telling you the rate of change like the shift in change of state. The second is secant, a measure of curvature. In Hooke's law it focuses value from the field into the spring. If you are talking energy from the field subject to weak mixing, that angle applies to the secant to establish the focus of position=mass. Equilibrium for a set is defined by its curvature.

man.... Thank you!!

Position, velocity, acceleration, jerk, snap, crackle, pop. Done, lol.

Derivatives like zoom in zoom out Your eyes adjusted to see correct shape

This is just d/x^2

Oh my god is this how they teach this in other side of the puddle? Don't you talk about velocity and acceleration?... For me the first derivative value in x0 it's just the coeficient for a line (g(x)=x) to be tangent to to f(x0). And, by extension, the second derivative of x0 is just the coeficient (if more stretchy, wide, or upsidedown) for a parabola to match the surrounding of f(x0). For example the second derivative of x³ and I beg forgive my unrigurous and unproper vocabulary I'm half asleep also english is not my first language: - Approaching to x=0 from the left it wildly comes from minus infinity to getting gradually less wild as a parabola, so the values must go from a wild inverted parabola (-2x², -1x², ...) - On x=0 well it pretty much looks like a flat line so (0x²) - Starting from 0 on, what's observed is the opposite, evolves like a parabola but gets wilder as you go further (1x², 2x², ...) Naturally, this evolves as a parabola getting wilder in the ratio of x, as x³ is x²·x so we can see the second derivative of x³ is x (-2, -1, 0, 1 ,2) and pretty much I can have an easy idea of this when I see whichever function. And specially if these define physical phenomena: - For example where can you find systems where a variable works with parabola-like things? (Simplyfying) Driving a car and stepping on the accelerator. If you press the accelerator slightly the position of your car evolves as a parabola (ignoring friction with the surface). The second derivative of your car position is how hard you press the accelerator. The same for the brake which would be a negative constant value (until the car stops). I must admit I just watched half of the video (and I am sorry) as I saw this was getting so complicated for something that, in my point of view, can be explained so easy. I still can't believe that the examples here presented are not ideas that the normal college student don't associate naturally with the derivatives. So if I am wrong forgive my arrogance and please show me what reality is. About third an so on derivatives, they would be "How much of a x³ is the surroundings of f(x) here?" but being x³ flat in 0 well they don't provide much useful information really, unless you're talking about velocity where exist the concept of overacceleration and other more specific cases. The same for the rest.

Given a norm, the length of a vector is the same under every basis, and since we must also satisfy that the probability adds to 1, assuming that length = 1, it seems convenient to define the probability function as ci*·ci such that it adds up to <ψ,ψ> = ||ψ||^2 = 1. Less formal, but perhaps easier to understand.

Great explanation. Explanation of why linear algebra in QM is so simple and intuitive. Really cool.

can anyone give me a link to Feynman's lecture.

Any hint about what you’re getting at with the final example? The heat equation one is intuitive to me but not sure what is meant about higher energy being related to shorter wavelengths. Is it something to do with the higher curvature at the crests of the waves for shorter wavelength?

my friend, we are eager to complete the series in quantum. waiiiiiiiiting for you

The idea of an "instant" really perverted and damaged our mathematics.

The rate of change of the rate of change. Example: The rate that the acceleration of something is changing.

OMG worth every second. And probably then most beautiful seconds of my life. The Beauty of quantum physics can't be explained better than this.

Very cool! I was thinking about how to think about the first derivative in this way and I'm thinking that it's like the average of the points on the positive side minus the average of the points in the negative side. I haven't done the analysis in the same way to verify that but I do really like this alternate way of thinking about derivatives.

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Electronics. RLC circuits.

You think people don't understand a derivative but understand taylor series expansion?! right.. that makes sense..

When i was in my undergrad,my thingking the first order tells u the distance, the 2nd order tell u the area, the 3rd order is the volume....

The second derivatives fails me in mathematics and physics. 😅 So i tried the laplace transform.

change in energy drives time evolution… and change in momentum drives spacial transformation… that’s astonishing, never thought about this approach in understanding the quantum states being described by this equation!

Physicists: let’s just Taylor expand it and see what it leads to. Mathematicians: why the hell is this differentiable?

#Newton was an #ET stuck in the year 1600 mathematically fiddling on the side of his main passion … #Alchemy. And, from this isolated stimulation arose his masterwork, “The Principia” after a swift kick by Sir Haley, he of the comet’s orbit calculation problem, which #Newton had solved. But, only after inventing (or, discovering) the math from the #Alkashic-records that solved the problem. 😊 8:17

So, the function f(x) varies in direct correlation to the movement of variable (x). And, to what relative amount of movement the variable (x) moves, the function f(x) moves, as well. Could be (1) to (1). But, in this example … the expansion of the function f(x) appears to be greater than the movement of the variable (x) as if the function is representing a curve f(x) with a focal point of (x). Do we know the radius of the circle now? 😊 2:50

A trip to Harvard, Massachusetts across the Charles River bridge heading due west. “One if by land, two if by sea … Three if by Russian troll farm!” 😊 1:46

#Wave-functions, #Quantum-tunneling, #Quantum-computing, #Heisenberg’s Uncertainty Principle, #Quantum-entanglement, Etc. “Indeed!” 😊 1:40

#HQI = “Harvard Quantum Initiative”; 😊 1:20

This very similar to definition of epsilon proving

Fills the void between first and third derivatives?

But laplacien symbol is tourned (or my be in your country you allways use it different? Usually, laplacien is represented by upercase delta.

I think this video explains the meaning of the second derivative, but it does not tell us why nature behaves this way, am I right?

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By evolving backwards in time, i believe you meant we can back track to find where is was.not we go back in time. So i see! Breaking time symmetry means we can not back track Which state it was in!

I see! So if position Does not change, There is no momentum. When we are certain There is a momentum, the position has changed so we don't know where it is! Like wise, When we are certain of the position(no change in position,fixed?), momentum has changed so we don't know what it is?

also, why high energy waves have lower amplitude?

You provide direction you have mathematical derivatives as differentials.

It also gives the maximum and minimum energy contributed as the second derivative is zero.

this is so powerful!! It's like saying momentum and energy are same thing. While momentum and position are different thing!

Can you make a series of videos on various interpretations of QM? I have read the Helgoland and I love how Carlo has described the relational interpretation, would love understand the intuitions behind other interpretations!

The sign Equal should not be used since any derivation included a constant.

6:36 this is what we were taught to find the maximum or minimum value of a function