Taking the quantum brick road. "Do I turn right or left here?" "Yes."

@chinkeehaw9527

4 жыл бұрын

Michael Price This is a technically correct answer. The actual question that shows the weirdness of quantum mechanics is: "Did you turn left and right?" "Yes."

@donwald3436

4 жыл бұрын

Same answer if you ask a computer scientist.

@sphakamisozondi

4 жыл бұрын

It depends, do you have a Heseinberg license? Lol.

@justmehere_

4 жыл бұрын

wow never noticed that meme is a superposition but yes it is

@tiny_toilet

4 жыл бұрын

@@donwald3436 Computer scientist does both and tells you which one you did....unless there was a loop, and he blows his stack instead...unless Win95, in which case, BSOD.

A side note for those interested in the math: We don't use sine and cosine just because "they look wavy." We use them because there's a piece of mathematical machinery called the Fourier transform which let's us write _any_ periodic (aka wave) function as the sum of sine and cosine functions. It's incredibly convenient to be able to represent _any_ possible wave function in terms of just two relatively simple functions, so that's why we use them. 3blue1brown did a video explaining how the Fourier transform works for anyone who wants to know the details: kzread.info/dash/bejne/paSJsNKydpiecrw.html

@cedmelancon

2 жыл бұрын

Discrete Fourier transformations in signal processing has to be the hardest maths I’ve had to do in university. Typically I tend to be able to make a mental image of what I’m doing in maths and make my own way of understanding it, but my mind couldn’t make sense of these, I had to stupidly learn these by heart.

@ankitaaarya

2 жыл бұрын

@@cedmelancon that totally sucks. what learning by heart means?

@rustycherkas8229

2 жыл бұрын

@@ankitaaarya "Learn by heart" is an English 'idiom' that means "rote learning"... It's like navigating in a city in a foreign country where you cannot read ("understand") street signs, but learn to get around "mechanically" from memory. That's your fish feed for the day. (A reference to another English idiom that begins: "Give a man a fish; you feed him for...") The "fishing lesson for your lifetime" gift is to point out to you that you are connected to the World Wide Web, and can search out answers to questions like this for yourself... Happy fishing!! :-)

@timseguine2

2 жыл бұрын

A side-side note for those who are really interested: Sine and cosine may be particularly nice functions with this property, but there are an infinite number of alternative bases that can look arbitrarily weird which all have an analog to the fourier transform. Picking sine and cosine is exactly analogous to the choice of basis in finite dimensional vector spaces, that is to say entirely arbitrary and without consequences. So to be perfectly correct, we use sine and cosine entirely because we like sine and cosine. For some people that might be because "they look wavy".

@NotAGoodUsername360

2 жыл бұрын

It can also be explained by the fact that all waves can be simplified into an infinite series of right triangles, in the same way a line is an infinite series of points, hence the sudden appearance of trigonometry.

your skills on teaching are the most outstanding qualities a person can have.

Not only did this help me understand quantum mechanics better, it helped me understand probability and statistics better, or gave me ideas for how to convey it to others. There's a lot of power in the term "skinny rectangles" especially for helping students transition from discrete probability distributions to continuous ones.

@louisrobitaille5810

10 ай бұрын

Those skinny rectangles are one of the most basic concept in calculus 👀. Adding them all up is how integrals work 😁.

Skinny rectangles = Calculus by stealth. Nice job Nick :)

@NoActuallyGo-KCUF-Yourself

4 жыл бұрын

Archimedes was pulling that trick thousands of years ago.

@william41017

4 жыл бұрын

I read that this is an old concept, known as infinitesimals, mathematicians just didn't like it very much because it wasn't very rigorous.

@anarchistsspit4483

3 жыл бұрын

Skinny rectangle infinitecimals are beginners beliefs. Calculas outgrown a lot from this now a days.

@hybmnzz2658

3 жыл бұрын

@@william41017 not true. Calculus was informal for more than a century. Cauchy, Weierstrass, and others made it rigorous when they needed to but the smartest minds often cheat a little.

@gordonlawrence1448

3 жыл бұрын

You have to do the "skinny boxes" method for mathematical models if you are using a spreadsheet EG calculating the voltage on an analogue integrator.

_“The events are probabilistic. The probabilities are deterministic.“_

@ScienceAsylum

4 жыл бұрын

Oh, I like that! Where is that from?

@teefkay2

4 жыл бұрын

The Science Asylum My old QM professor from college. 1974.

@ScienceAsylum

4 жыл бұрын

I'm stealing it.

@Ortorin

4 жыл бұрын

In more lay-terms: What happens to a quantum particle is completely up to probability; it might be here or there, it might be going this fast or this slow. That probability is set in stone, which means we can tell what the probability is if we measure. We can always tell what a quantum particle might be doing, we can never predict what it will actually do. (Kinda like a crazy relative. You know what they CAN do, you never know what they WILL do.)

@StanleyKowalski.

4 жыл бұрын

probability of a event of a wave to occur at sea surface is 1, but to know exactly when and where is deterministic. not sure of that example fits the above statement

this is what I like about these videos. Even if you don't learn anything profoundly new sometimes, when you see a good animation changing from one aspect to another, two previously separate things get connected and it clicks. A new level of understanding!

@ScienceAsylum

4 жыл бұрын

Static diagrams just aren’t enough sometimes.

This is the best explanation of quantum wave functions that I ever seen. I've seen a lot of videos from a lot of KZreadrs and this is the only one that is actually understandable by non physicians. Great work!

@neoness1268

Жыл бұрын

totally agree with you

@88feji

Жыл бұрын

You mean "physicists" ... (physicians are medical practitioners) ..

@kylecesar6347

Жыл бұрын

@@88feji no, only doctors understand wave functions

@Zeus-rk5yy

9 ай бұрын

@@kylecesar6347 😂😂

This is the most intuitive explanation I've seen so far for laypersons like me. I've seen so many videos say, basically, "You get the probability by squaring the wave function." OK, so what exactly _is_ the wave function? "It's a probability thing." Which doesn't feel very helpful.

@tom_something

4 жыл бұрын

@Fuert Neigt He's got a ton of really amazing videos. Don't forget to subscribe!

@Blox117

4 жыл бұрын

@Fuert Neigt _anything_ you say? hmm...

@l1mbo69

3 жыл бұрын

How was his answer any different? He did expand on it more but his final answer was of course the same, that it's a probability thing

@xiaoxiao-kg5np

3 жыл бұрын

Tom, You should know there is more to this story. Intelligent people have long ago figured out that Quantum theory is all BS. Same with everything that the so called "genius" Einstein said. All total BS. Keep that in the back of your mind when things seem weird, this is the reason.

@tom_something

3 жыл бұрын

@@xiaoxiao-kg5np classical (pre-Einsten and pre-Quantum) models do not explain observed phenomena. Is there a different model you can offer, or is this just filed under "who knows?"

Descartes is at fault here, he was the one who coined "imaginary numbers" as a derogatory term. Gauss knew better and named them lateral numbers.

@ScienceAsylum

4 жыл бұрын

Yeah, I mean, technically speaking, all numbers are imaginary... but these are the names they have now. We're stuck.

@Bodyknock

4 жыл бұрын

Which goes to show, people who haven't taken a class about them and think complex numbers are a hoax are putting Descartes before the course. ... I'll show myself out....

@NoActuallyGo-KCUF-Yourself

4 жыл бұрын

How "real" are real numbers, anyway?

@NoActuallyGo-KCUF-Yourself

4 жыл бұрын

Descartes also had that pesky duality problem. Princess Elisabeth of Bohemia asked him some good questions about it.

@channelnamechannel

4 жыл бұрын

@@ScienceAsylum natural numbers are real. the others... i'd say not...

This might be the best layperson-accessible video on quantum mechanics I've ever seen

Max Born is one of the unsung heroes in science, 'cause his interpretation in 1926 of wave function as a probability function was groundbreaking at that times!

@Geokinkladze

Жыл бұрын

Surely his greatest contribution is Olivia Newton John.

@dvoiceotruth

Жыл бұрын

he did get a nobel prize for that. there is no unsung here. if you want to know about an unsung hero then look for S.N Bose.

@bobespirit2112

8 ай бұрын

Wait - Max Born or Max Bohr? Oh, it’s Neils Bohr…oops

@bobespirit2112

8 ай бұрын

@@GeokinkladzeWait..what? I don’t get the connection…?

@bobespirit2112

8 ай бұрын

I looked it up - she’s his granddaughter from his daughter Irene. Well, I’ll be damned - definitely his most important contribution to humanity!!! 😂

Underrated moment in this video was when Nick made sense of why we use sine and cosine: they make shapes that look like waves. Like, you need something to look wavy? Here, use this. Doesn't matter what that wavy thing is, but this will get you a pretty good picture of it on your graph, bud. Thanks.

@ScienceAsylum

4 жыл бұрын

You're welcome :-)

@NoActuallyGo-KCUF-Yourself

4 жыл бұрын

Fourier to the rescue!

@rzezzy1

4 жыл бұрын

Yeah, that's basically it. A more calculus-based perspective on this (which is the math we use to calculate these wave functions in quantum mechanics) is that a sine or cosine wave is "proportional to its own second derivative." Basically, they are curviest at their own peaks, in a very precise way.

@erdemmemisyazici3950

2 жыл бұрын

This was a great explanation. It's all gradience, until it isn't.

@ronsnow402

2 жыл бұрын

@@ScienceAsylum A probability distribution is just another way of saying "We don't know what happens on a smaller scale". We have to be humble & say "I don't know what the constituents of this wave is, or if any", & continue doing science. I wish you would have added this in your video, physicist need to be more honest about the data to avoid confusion... sometimes "I don't know" is the right answer.

Waaait, what? Yesterday i was searching something on this topic and meanwhile i was thinking "man, i really hope the science asylum will release a video on this". Nice

@ScienceAsylum

4 жыл бұрын

Glad I could deliver :-)

@Secret_Moon

4 жыл бұрын

@@ScienceAsylum can you do a video explaining how the waves of two (or more) separate particles can interact with each other? I understand the nature of the quantum wave, but how can the waves from different particles interact to create the interference pattern, especially when they are separated by time like in the double slits experiment?

@NovaWarrior77

3 жыл бұрын

You're his clone you, just don't know it.

This man just casually explained the entirety of high school level maths in a single 11 minute video.

That was a great description of the QWF. The graphs really clicked the issue into my mind. I love the humour and general presentation of the video. Keep up the excellent work, videos like this should be compulsory in all physics courses. Cheers

I clicked on the video for science and stayed for .......... SCIENCE!!!!! Your explanation is amazing !!!

damn, that boxxy reference brought ME down to memory lane.

@addajjalsonofallah6217

4 жыл бұрын

Ah yes queen boxxy

@poe84it

4 жыл бұрын

@@addajjalsonofallah6217 aaand it's 2008 again!

This is the greatest quantum video ever explored in youtube video or any platform. You just hit it. Thank u thank you so much Nick.

I have to say, I watch a lot of physics videos on KZread. Yours are great but the thing I like the most about them is that somehow you manage to figure out exactly the question I have, title the video as i would, and cover exactly what I needed to know to feel like I got my answer. Well done! At least for me, which may mean nobody else gets any of it. Hmmm. Well, I luv ya, so you have that!

for me , this is your best video..... quantum mechanics looked simple in this

@shanm4629

3 жыл бұрын

I felt so.

As Richard Feynman said, "The prize is in the pleasure of finding the thing out, the kick in the discover"... Ya this video gives that required kick....

@jcf20010

4 жыл бұрын

He also said... If you think you understand quantum mechanics, you don't understand quantum mechanics. - Richard P. Feynman

@ADogNamedElmo

4 жыл бұрын

@@jcf20010 stupid quote

@jcf20010

4 жыл бұрын

@Jerry Perry I under stand it. The quote works on different levels. Kind of like this one: "You can observe a lot by just watching." -- Yogi Berra

This was by far one of the best explanation of the wave function i have ever seen.

This madman is teaching about the basic idea of integration without letting the people watching the video know (which is probably good since you are trying to explain quantum wave functions in a simple way at the same time). Also, I finally noticed that 3Blue1Brown plushie on your shelf, nice!

@nibblrrr7124

4 жыл бұрын

[bernhard riemann, stroking his beard in begrudging acknowledgement like a kung-fu master]

@billusandda5845

2 жыл бұрын

@@nibblrrr7124 lol

Very happy to see you after a long time explaining Quantum wave function. Your explanation is absolutely amazing.

Shit has started to become real on this channel , you are getting sponsors . Finally!!

thank u so much for taking care of my curiosities so well, have just fallen in love with this channel

Such a great video Nick. I love your vids they are always conceptually rich and plenty of good questions

Love your videos. You go straight to the point, and cut the bullsh*t metaphores or theoretical explanations. It's very refreshing. Thanks !

I really love how you animated the electron as trying to be at every position at the same time, but still keeping it as a particle. That is the best visual representation of a wave particle duality I ever saw.

@360wheelz5

4 жыл бұрын

Indeed!

Nick you're getting better and better. Just loved your video. Best explanation I've seen since learned this in 1993!

I don't know if I learned anything, but I do enjoy how you present your material. You are a great teacher.

Android Robot kicking the "i" - LOL !

@narratordru7188

4 жыл бұрын

lol.. yeah

@NoActuallyGo-KCUF-Yourself

4 жыл бұрын

Kicked that i right in its a.

@vladimirpain3942

4 жыл бұрын

What else should it do? :D use it? Come on...

@mjproebstle

3 жыл бұрын

cheeky

Awesome work yet again Nick - thank you!

You're a lsegend for that one fam. You answered all my questions. Thanks brodaaa 🤜🤛

I absolutely love you man, may you live a long life. You make science exponentially easier! Thank you so very much

Maybe it's because I've learned complex nos before unlike many things you talk about, but you explained this topic extremely well. In my opinion, this is one of your best videos yet! I love your, hmmm, "energetic" style 😂

Good job taking us one baby-step at a time through a complex subject.

I've said this before, but the thing I really love about your videos is that I always learn at least one new thing! This time, it was that the square involved in the Born rule is a *complex* square. I've seen many people write about the Born rule informally in comments here and there, but not ONE person has ever made that clear. Thank you!

@ScienceAsylum

4 жыл бұрын

You're welcome 😊

I love the fact that he literally said that he hate Quantum mechanics but still trying throughout the lecture to maintain interest on topic. that's the motivation I need to pursue my study 😅😅😅

Ur really best sir 💯 No one explained me quantum mechanics that deep and well

Mind totally blown this is what everyone means when they say it's the square of the wave function that gives any meaning to a quantum state

@ScienceAsylum

4 жыл бұрын

Exactly.

@NoActuallyGo-KCUF-Yourself

4 жыл бұрын

Isn't the square of the amplitude of a mechanical wave (or even EM wave) its energy? Is there an energy - probability equivalence? I remember Noether said energy and time have a symmetry, etc. But I don't remember the details. These quantum probabilities aren't just from functions of time (?) .. anyway, just rambling. Good observation.

@missingno9

4 жыл бұрын

@@NoActuallyGo-KCUF-Yourself You're right that the square of the amplitude is the energy, but that only applies for physical waves. Wave functions are basically mathematical constructs used to describe probabilities, not actual physical properties like displacement or field strength.

Dude, your videos are AWESOME! Keep it up man! Greetings from Bulgaria.

There is very less Probability that someone do not like your video. Its not so Complex task to subscribe and share your videos. Its time to get Real and start understanding the physics from this channel.

Really this channel is so underrated! It deserved more subscribers. Let's make it popular!

When you say at the end “Until then, it’s ok to be little crazy” I really feel very reassured. 😆

Thanks that was one of the most comprehensive explanations I have heard.

My god you are the best explainer among KZread 😌😌

Not the first one, but I'm certain I'll love it. Love from Nepal!!

One comment i would make is to show an example of a textbook picture of the cos and the isin and relate to the actual rotating wave function. Other than that, this is one of the best explanations I've encountered as to what the wave function "means"

It's one of the best videos I have ever seen..makes understanding things way simpler..thanks!

You are a life saver. Keep making these and adding the humor. Saved me from tears over chemistry

wow just found this channel today, goldmine! Its been hard being stupid but interested in what smart people are interested in, i've seen a few of your videos now and been able to follow everything, gotta say thats a first after many years of youtube, well done man! (And you're funny, 5:47) They say you dont really understand something until you can explain it easily, so you must *really* understand what you're talking about! unlike most other youtubers!

I think I've watched about every video on the wave function. This is the first or at least best I've found in showing how it actually works-what is actually does. I know how F=MA works, and I knew the wave function is the quantum analog of the F=MA, but I could not understand how the wave function predicted the future state. I did not until now understand about the different inputs for each property. I would like to more about what those inputs actually are so I can understand how it operates better. But this video advanced my non-math physics learning quite a bit. Thank you.

@fulanotu6611

6 ай бұрын

The imputs are displacement, time and frequency

I am so grateful for all you have done for us!

1:37 that boxxy reference made me so happy

I love that *transform* sequence! I imagine inserting such clip into our software at work... ;) The whole vid is great too, of course.

@ScienceAsylum

4 жыл бұрын

It's a nod to the Adam West Batman transition 😊

Quantum Mechanics has always seemed to be really strange... but you make it sound much simpler than I made it out to be. Thank you for showing the connections between probabilities, complex numbers, and integration to understand how those functions work. Awesome job! Although Quantum Mechanics will almost certainly still be a challenge, you made it seem less terrifying. So thank you for that.

@ScienceAsylum

4 жыл бұрын

You're welcome 😊 Glad I could help

@Lucky10279

Жыл бұрын

The _math_ of QM isn't actually that hard to understand -- it's all just calculus, linear algebra, linear differential equations, and basic probability theory. And, while those can certainly be challenging when you're first learning them, it's all standard math that's covered in a typical undergrad math or physics degree and is nothing specific to QM in particular. The truly challenging part is distinguishing between and relating the math, the experimental results, and the various interpretations. It's figuring out what, _if anything,_ the math actually tells out about individual particles that's so hard.

Still killin'it, Nick. Thanks a million.

Brilliant as always! Amusing and highly informative.

"i" really get your joke.

@daves2520

4 жыл бұрын

Good one.

@mikey20is

4 жыл бұрын

justa actually, that's about the only thing I did get. I watch his great vids for humility with a snippet of once and a while " ah ha "

@mito._

4 жыл бұрын

underrated!

@tiny_toilet

4 жыл бұрын

i^2 don't.

@davidwuhrer6704

3 жыл бұрын

@@tiny_toilet Jay does, but he's an electrical engineer.

Made my day to see a new upload from the asylum

@narratordru7188

4 жыл бұрын

Mine too

@erikawanner7355

4 жыл бұрын

narrator dru ditto!

Good stuff, clear and short enough. Thanks!

Amazing. how a 10 min video can explain more than phd quantum mechanics professers who took 7 years. keep going :D

This was great! And the dance music made it seem like a party.

So THAT's why I had to learn calculus!

An excellent way to explain it. Thanks for the hard work you put in this video

thank you so much. really it help me a lot. keep going on for spreading nice information like this.

ohh yeah, great to see edutubers that aren´t afraid of showing the math, specially for my current introduction to quantum mechanics course xdxd. Instant subscription and if you can talk about Hilbert spaces that would be awesome!!!

@nibblrrr7124

4 жыл бұрын

Yesss, I'd also love to know what's the deal with Hilbert spaces. Or to get away from QM, how the heck do you (even begin to) describe spacetime curvature in numbers for GR? Or, how does Hamiltonian mechanics work, and how is it different from Lagrangrian? And anything along the lines of your recent div-curl-Maxwell/Heaviside episode would be _amazing_ - visualizing the important consequences of mathematical equations (though I realize that format is a tall ask ^^)

I've got a feeling, after you assemble all your best explanations in its best sequence, I will FINALLY UNDERSTAND HOW THIS WORLD WORKS!

@aniksamiurrahman6365

4 жыл бұрын

OMG! So as soon as Science Asylum finishes producing all its videos, you'll take over the world!

@kev4ev

4 жыл бұрын

@@aniksamiurrahman6365 That was the plan!

Nick, You mean you are not just going through the science experiments books and do another video that 50 other youtubers are doing over and over? I do love your fresh view on things. Keep it up. You have insights that are worthy.

@ScienceAsylum

4 жыл бұрын

If I'm not adding something new to the community, what's the point?

THIS IS AWESOME OMG IVE BEEN SO CONFUSED FOR SO LONG THANK YOU

9:42 Absolutely!

this one was bit extra crazy :) i like it . laughted loudly around 6:00 - 6:20

Thank you for reinforcing that this is a mathematical function and not a physical property. No one has put it in those words and that is the concept I have struggled to grasp

I forcefully convinced myself that I understood the video. Thanks for your super awesome explanation. Nobody does it better than you.

Great video as always. Measurables go in, probability comes out, with Hizenberg limitations on certainty. No need for observers, or consciousness, or any woo whatsoever.

@lopezjraul

2 жыл бұрын

The understanding of the behavior of the quantum particle as a probability without any understanding of where it comes from is derived from the quantum wave function. This is true and no need for any speculation to assert that. However, where does the quantum particle arise from? Or perhaps another question would be what is the nature of the quantum particle? Not what is the behavior of the quantum particle but what is it actually made up of? We called a wave but what does that mean as being defined in terms of its make up. Not advocating for woo here but it still doesn’t answer some important questions.

@rc5989

2 жыл бұрын

@@lopezjraul My opinion is that a quantum particle is best understood as a discrete deposit of energy into a quantum field. This is pretty far down the philosophy of science rabbit hole, but the only remaining undefined term is ‘energy’ and that is both basic, yet does not have a formal definition. If we accept ‘energy’ then the definition is also acceptable. All my opinions.

Hey, just wanted to let you know that this is fucking brilliant and one of the most "intuitive" descriptions on the topic I've ever seen

that square of wave function was ground breaking realization for me, thanks, exactly what i needed

This video helped me a lot in understanding the wave function. Very good .

This is Quantum mechanics for dummies to pro! Beautiful!

"bouncing squirrels arent the only waves in nature" i learned something today

Love your videos dude keep it up.

I just love your thought process and sense of humor, makes learning so much more engaging and fun! Although I got lost at complex square so going to research more about that, if you can do a video on how quantum wave function relates to quantum entanglement I will love to know more!

@ScienceAsylum

Жыл бұрын

Quantum Entanglement: kzread.info/dash/bejne/mp2trdqhdbe-lJs.html 🤓

Nick: "did this help you understand quantum mechanics a little better?" Me: LOL... like I come here for understanding 🤣

I love your content. your videos help me escape my crippling depression for a short time & for that I thank you. I have a question about the perspective of a photon. from the perspective of a photon does time stop?

@ScienceAsylum

4 жыл бұрын

You could say that, but I think it's more accurate to say the photon can't possibly have a perspective. Nothing traveling at the speed of light can. A perspective requires a rest frame and photons don't have one.

That was beyond awesome. Well done

One of the best and beautiful explanations about quantum mechanics on the title: quantum wave function. Nice boss👍

Quantum mechanics hurts my brain in a fun trippy way

@AdamAlbilya1

4 жыл бұрын

Quantum mechanics entangles my brain a PARTICULarly fun way.

@tuck295q

4 жыл бұрын

My head feels wavy 😖

Can you use some details from this video to explain the Pauli Exclusion Principle?

I love your channel! It's really fun to watch, learn, and also hurts my brain too, but that's fine that's how I learn.

Oh my god .... It's probability of being helpful is really high..... Helped me with deeper understandings...

*_The Born Rule_* starring Matt Damon as - no wait, wrong Bourne

7:55 "Just give up" But we all know that you won't.

This was a fantastic video. I've been studying machine learning lately, and this actually helped with understanding some of the underlying mathematical concepts there, as well.

@ScienceAsylum

4 жыл бұрын

Cool!

this video helped me a lot to develop the idea of wave function as i am newly introduced to this..thanks

I've been watching your videos for about 2 years and yeah I have really learnt a lot And till now I've been ''crazy'' so far🤪🤪🤪🤪 👍👍👍👍👍for ur channel Okay I still do have the following questions; 1. Where the heck does the energy come from in the process of nuclear fission and fusion???????😰😰 Mass defect or nuclear binding energy???? 2. Nothing.... that's all 3..........''let's all be craz😜😜🤪🤪🤯🤯🤯

@ScienceAsylum

4 жыл бұрын

Yes, the energy released during fission and fusion is nuclear binding energy... sort of. Technically, nuclear binding energy is negative (a loss). A bond is loss of energy that traps particles together. Here are a few videos explaining that if you haven't seen them: Nuclear Fusion Explained: kzread.info/dash/bejne/fn-JsqOkZZOaabA.html What EXACTLY is a Bond? kzread.info/dash/bejne/n3p_pbmYdJXVdZc.html Bonds Do NOT Have Energy! kzread.info/dash/bejne/mWdt0NmHnZO-lto.html

Awesome man. Even I'm starting to understand the horrible quantum probabilities.

We are currently doing intro to quantum in lecture now. Really up-to-date with my physics study! ❤️❤️❤️❤️

The way you explained is amazing