The True Meaning of Schrödinger's Equation

Schrödinger's equation governs the behavior of tiny quantum particles by treating them as wave functions. But is Schrödinger's equation actually a wave equation? Maybe not.

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TIME CODES

00:00 Cold Open
00:24 Viewer Question
01:02 Strings
02:41 Wave Equations
03:42 Where does it come from?
04:43 Schrödinger's Equation
05:29 Language is Complicated
06:28 Arvin Ash Collab
07:36 Heat Equations
08:18 Probability Flow
09:56 Summary
11:02 My Book
11:17 Other Quantum Equations
11:48 Outro
12:00 Featured Comment

#quantummechanics #quantumphysics #schrodingerwaveequation

[stevenjones]

Dang, a flow of probability makes a lot more intuitive sense to me than a wave of probability. Thanks for the awesome video!

[shelley-anneharrisberg]

This is the first time I have really understood why the wave equation is written as it is! We did the derivation and how to solve it, but I never fully understood it. You are an epic genius at understanding and relaying physical concepts! The same for the heat and fluid equation and explaining the "flow" of probability in the Schrödinger equation. I am so grateful :)

[Culando]

"By the way it's actually a hundred times more complicated than that" seems to be the motto of Quantum Physics. And the collab with Arvin Ash is awesome! I've checked out a number of his videos too.

[devarshnayyar]

This is the equation we all can understand without understanding it.

[Psychx_]

I'm from Austria and I'm also a Schrödinger fan. Before the country transitioned to the Euro, the currency was the "Schilling" (read 'sch' in German words as an 'sh' in English, i.e: shilling). The second last iteration of said currency (in the 80's up until the 90's) had Schrödinger and the wave equation on the 1000 bank note. Ofc I had to get one :P
It contains a portrait of Schrödinger, the formula symbol of the wave equation and a stilized atom on the front and the main university of Vienna and another stilized atom on the back. For anyone who's into collecting old currencies, I can highly recommend getting one. It's an absolute beauty of a bank note.

As a side note, these cannot be exchanged into Euro at the Austrian national bank anymore, but they become increasingly sought after by collectors. If you keep one for 40 years and have it remain in good condition, it may also serve as a nice investment.

[tf]

Thanks Nick! This semester I’m taking my first proper rigorous QM class! Perfect timing!

[AlecBrady]

This is great! I learned recently (from 3Blue1Brown, actually) that the Fourier transform originated in Fourier's contribution to solving the heat equation, not the wave equation; so the role of Fourier transforms in QM now makes a lot of sense. Thank you for this!

[CT-pigl]

Man, what a fantastic summary of some of the main relationships in physics. That free body diagram of the string section related to the equation terms was particularly clarifying.

[Schraiber]

I actually used the analogy between the Schrodinger equations and diffusion equations (which generalize the heat equation) as the key to my PhD thesis, where I applied path integration methods from QM to population genetics problems that are usually described with diffusion equations

[johncourtneidge]

Thank-you!

As someone who encountered Schrödinger etc as an Undergraduate at The University of Bristol fifty--five years or so ago, I'm intrigued by the fact that this presentation weaves in modern cultural forms of the entertainment industry.

All most interesting!

Again my thanks!

[ToriKo_]

“The wave equation isn’t about wave shapes, it’s about wave motion” 10:05 great line

[dimzen]

I haven't watched you channel for years, and now overwhelmed by all - level of disputed problem, simplisty of explanation, and even an artistic level

[SergTTL]

That boxy wave radiates some old school vibes. A signal from a distant past.

[joepeach]

“Where was I”? My thoughts all through this, and loved every second of it!

[dmiller]

"Curviness determines acceleration"
"Probability flows through space"
Love these

[astradrian]

First-year physics undergrad here and I was just studying these equations! Love your videos Nick; you're one of the reasons I'm studying Physics today ;)

[macronencer]

You are brilliant, Nick! Almost every time I watch one of your videos I either learn something new or gain a new perspective. This was really helpful - thanks!

[vincentwalker]

Actually, I watched Arvin last night, February 2, 2023. Thank you for putting it all together.

[RalphDratman]

Yes the Schrodinger equation is first order in time, like the heat equation.
But the i factor, by rotating the time derivative by 90 degrees, makes the result very different.
In fact, if you split psi into real and imaginary parts, you can write two differential equations, then combine them to finally get a single differential equation that is second order in time.
That is, if I remember correctly.

[reinhardtristaneugen]

Zur Heterogenität dessen, was man nomine so in der Quantenphysik vorfindet:
Die Gleichung H Psi (r) = E Psi ( r ) ( das Psi für die Wellenfunktion... ) ist in dieser Form der Schrödinger-Gleichung eine Eigenwertgleichung, wobei ihre Lösungen also Eigenfunktionen zum Eigenwert E ( wer nicht weiß, was das ist, der sich sehe sich die Hauptquantenzahl < n > an... ) sind. Weil die Eigenwertsgleichung meistens nur durch diskrete Eigenwerte in Abhängigkeit der Randbedingungen erfüllt wird, heißen diese quantisiert als Antonym zu kontinuierlich.
Ich finde aber das Problem ist, dass, wenn die Leute fragen < quantisiert > was'n das? ...die Antwort < es sind infinitesimale Pakete dessen, was das jeweilige Quant ist, einem zwar Ruhe bringt... ( ...die Leute hauen ab... ...sie hauen aber auch bei🖕ab ), aber keine abstraktionsorientierte Antwort sein kann, weil die Leute autosuggestiv wieder an Teilchen denken und nicht von dieser Anschauung aus dem Mesokosmos wegkommen.. ...Rettung vor dem, was die Sprache der Physik ist, bringt einem eigentlich nur der mathematische Term als Hilfsmittel der Beschreibung aus dem Reservoir, was die Mathematik abstrahiert aufgespannt hat... als letzte Zuflucht für die, die da die Schöpfung so gut wie möglich sehen wollen... ...ich will hier so schnell wie möglich
Le p'tit Daniel🐕🐕🐕🏒🏒🏒