Wave Functions in Quantum Mechanics: The SIMPLE Explanation | Quantum Mechanics... But Quickly

Ever heard of the term "wave function" in relation to quantum mechanics? What does it mean? How is it interpreted?

Hey everyone, I'm back with a new video! This time, we're going back to basics and understanding exactly what a wave function is, as well as what it represents, in the world of quantum physics. This video is going to be the first in a series I'm going to call "Quantum Mechanics... But Quickly". In this series, I want to discuss some fundamental quantum concepts, and explain them in as visual and intuitive a way as possible - without having to sit through an hour long lecture, or understanding complicated graduate level mathematics.

A physicist named Louis de Broglie once suggested something amazing. While scientists were busy debating whether light was a wave or a particle, de Broglie suggested that even matter - things with mass (e.g. electrons, protons, atoms, etc.) - could behave like waves. This idea was revolutionary due to the mountains of evidence scientists had up until that point that matter behaved like particles. However, the quantum world was soon to revolutionise everything we thought we knew about the universe. And as it turns out, de Broglie's suggestion was right.

His suggestion of matter waves permeated into the work of Erwin Schrodinger. Combining the idea of matter waves with the principle of Conservation of Energy, Schrodinger came up with the equation we now know as the Schrodinger Equation. This ended up being the governing equation of quantum mechanics, and crucially contained a function known as the wave function. This wave function contained mathematical information about any quantum system we happened to be studying.

The key question, then, was about what the wave function actually related to. What did it correspond to in real life? How should we interpret it? Well, there are a few different interpretations of quantum mechanics and how it relates to our real-life universe. The most commonly accepted one is the Copenhagen interpretation. And this interpretation suggests that a wave function is directly related to the probability distribution of a system. Specifically, if we take a system's wave function and square it (well, technically if we take its square modulus), then this will give us the probabilities of various results occurring when we make a measurement on a system. For example, the wave function of a system could tell us the probability of finding a particle at a certain position in space. Or it could tell us the probabilities of finding different spin states when measuring the spin of an electron, for example.

In this video, we discuss these examples in detail. Additionally, we briefly look at the consequences of wave functions having imaginary parts. Lastly, we look at how the Schrodinger Equation (or at least the time dependent Schrodinger Equation) governs how a wave function changes over time - apart from when we make a measurement on the system. This measurement causes a discontinuous and jarring change in the wave function, known as the "collapse of the wave function". This collapse has caused many philosophical problems for physicists over the years, and it continues to do so to this day.

Thanks so much for watching this video! If you'd like to support me, please subscribe to my channel and hit the bell button to be notified when I upload.
Instagram: parthvlogs
Second YouTube Channel: Parth G's Shenanigans

[keppa]

Now I am in a state of both "confused" and "excited".

[soumyajitroy]

Being a physics undergrad, getting to revise the concepts in such interesting way WITHOUT TEDIOUS DERIVATIONS is a blessing ❤️ thank you so much. Your explanations are amazing!!

[BenjaminTMilnes]

Schrödinger: 'I've come up with an equation that's good at describing hydrogen atoms.'

Dirac: 'I'm gonna end this guy's career.'

[joshuamunson]

Something that blew my mind about the collapse of the wave function through positional measurement is that a free particle can be theoretically anywhere in the universe until you measure it.

[shanmugamshans]

Hi parth you can introduce some math also in this series which we would love to see.🙏

[linezero]

I make a living on explaining what the wave function is. I am happy to see that there is finally a reference video giving a quick dirty introduction. Love your video, keep it up!

[nerffan]

You've managed to explain briefly what my QM professor couldn't do in my QM courses. QM undergrad really flew past me - I somewhat understood the math (as always, math is just following rules), but had no idea how to interpret it. Right now I'm applying to grad school hoping they don't penalize me too much for getting a C in QMII

[sanatanseconnection]

I am science graduate, seeking how to interpret the universe by physics and mathematics. You have done wonderful job, complex theory in so simple manner. I never want to miss you

[yxxshvs]

G stands for god in your name!
Amazing explanation...
I started building base of quantum mechanics by watching your videos before starting my syllabus

[bengriffiths]

One thing that blows my mind is that if you measure the particles position within that box in example 1, it will instantaneously collapse into a delta function (100% in one location) at that position which is obviously not one of the energy eigenstates (sine waves) shown. The bit that blows my mind is that in order to replicate this delta function in position, the particle instantly goes into a superposition of infinitely many energy and momenta eigenstates. This example is a great way to introduce commutation relations if you want to delve into the linear algebra in later videos

[eyewaves...]

pretty good short and relatively precise explanation with limited uncertainty !

[iziz]

I've spent much time reading and watching, trying to understand a bit about this equation. By just focusing on a picture of the wave, you have clarified what I was looking for. I won't forget this, but I will forget all the math derivations that I sweated through!

[sunithasomalingam]

I always wait for Parth Bro's Video❤️❤️

Now Wave Function 😁
Love dis Channel 😍

[ffhashimi]

Great Explanation!; I hope you extend this to a very simple system and explain how exactly physicists do there calculations, let's say a hydrogen atom what physicist do from preparing there experiment to doing there calculations until doing the experiment and finding the result; I know I may asking too much; but you are very good in explaining this topic and such a simple system example would put every thing said before into a very clear prescriptive; thank you for your excellent job!.

[surprisemokwena]

Me too. Guy sparked a glimpse onto something materially realistic yet mind bending

[jinggin]

You are the best Youtuber who totally grabbed my attention! I love the way how you put the quantum physics in, it is so fun!!!

[towhid]

It really helps a lot. Such a fun and formal way to enjoy learning such complex topics. Loving your work, Parth.

[mrscookiecutter]

thanks to you quarantine isn't as bad as it's supposed to be

[anonymes]

That's easily a contender for the best 10 minute explanation of the wave function i've seen to date. Concise and coherent (heh :).

Looking forward to further videos, especially about foundations of quantum mechanics (full disclosure: partly because my impression is you're not a fan of Copenhagen and i'm always interested in cogent arguments for other interpretations).

[abhishekaabhi]

Great idea video all about wave nature of electrons special feature as wave not just particle behaviour