Hi everyone! My goal with this channel is to intuitively explain the mathematical concepts behind quantum mechanics in a way anyone can understand. In the future, I look forward to making videos about other concepts in math and physics.
A bit about me: my name is Brandon Sandoval and I recently graduated from Stanford with a degree in physics. In Fall 2022, I am very excited and lucky to be starting my PhD in physics at Caltech. If you have an idea for a video or have any questions, go ahead and shoot me an email! Thank you for visiting!
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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.
/ᐠ｡ꞈ｡ᐟ\
Electronics. RLC circuits.
You think people don't understand a derivative but understand taylor series expansion?! right.. that makes sense..
This is for people who understand calculus, have a clear visual and conceptual intuition for what a derivative is, but just think of the second derivative as "the derivative of the derivative", which is a definition that intuitively tells us nothing about the original function. This video is building that intuition using the Feynman lectures at a base, which are all college level
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?
kzread.info/dash/bejne/hm2s0KWDhNXQfbw.html
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!
Which state what is in? A single quantum system is in no state whatsoever. The ensemble is in a state or, more generally, in a mix of states.
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
can you have 0 uncertainty in one quantity and infinite uncertainty in another? how do you calculate their product in that case?
Fantastic video series, I learned so much! I do have one question though; if the position wavefunction describes the coefficient of each position eigenvector, then how come it can take on complex values? Earlier in the series, you stated that the probability for each position value is equal to the amplitude squared, so why is it not the same in the position Schrödinger equation? Could someone please clarify this for me? Thank you!
Damn this was a great video
This is an awfully quiet video. I guess no one did a mic check.
at 8:48, when we multiply the two berackets, we got one identity operator from the multiplication of the two identitiy operators in both the brackets. don't we get another one from the multiplication of the dagger \dot U with \dot U? so shouldn't there be two identity operators on the right side of the equation at 9:01?
well done !
Smart, very cleaver~ it’s not my first time being amazed by how concrete the logic of math is and being amazed by people who come up with them! Nevertheless, being amazed by you for explaining it so intuitively and easy to understand. Thank you. Fabulous ~