วีดีโอ

I actually have this paper! It was a fairly quick read if I remember correctly. I even think Griffiths suggested this paper in the footnotes, I will have to check.

This is a very constructive piece of criticism! I genuinely appreciate the time you took to share your thoughts. You've highlighted key points that have helped me refine my approach to the "why do we care" segment. Your perspective on the differences between enthusiasts and students has also made me aware of my unconscious bias towards the student viewpoint. This feedback will be invaluable as I move forward, and I can incorporate a segment that addresses both audiences, such as "connections to the everyday world." Thank you once again for your thoughtful input!

@@ARBB1 decided to try something new 😂

@@curiousaboutscience yeah, it looks good

@@ARBB1thank you! So many options to choose from but it's fun to tinker. The chapter on the weirdness of QM needs a new TN design 😂🤓

@@curiousaboutscience A personal favorite book of mine is Asher Peres' "Quantum Theory, Concepts and Methods". I'd highly recommend it as a follow up after this one.

@@ARBB1 the description on Amazon is very promising! Thank you for recommending!

@@maxritter5642 multiply by i/i to get rid of the negative out front.

@@curiousaboutscience i also forgot that 1/i is equal to negative i

@@tunir3010 thank you! This was an good exercise to work through!

Nevermind 😅

🤣🤣🤣🤣

www.patreon.com/posts/partial-wave-low-111525745?Link&

This theory is so dense, but so much fun!

This sounds trippy, any good videos to check out on it?

doi.org/10.1119/1.3595554 I suppose I could download it and send it to you via email if you prefer that.

same question here!

Definitely not, this is algebraically intensive just to show the details. A computer program with these rules would spit out the combinatorically allowable states and you would reference a library with these functions and have them spit out the other values.

@curiousaboutscience Oh, thanks. Though that was not really what my question was meant to allude to. But I suppose the answer is yes then (with these quantities I meant the ones referred to in the three main questions).

@@sirmclovin9184 Got it! Yea, some of these are used, albeit, more numerically, because we can't always use "hydrogen like" models for all scenarios. Variations on multi particles models use similar concepts.

q(VxB) became qVB because they V&B are perpendicular so the cross product goes away. also qE is the force due to the electric field. so essentially the forces due to the magnetic field and the electric field cancel which is known as the hall effect.

@@matheusdepaula687 it's a beauty for sure! 🤓🤝🤓

These a fun ways to put the visuals from clever math people's heads into graphics. So darn amazing!

Yeah, sum/difference identities!

That is an important question! Thank you for asking - sometimes these questions are needed for understanding but are never asked so I am grateful you did! As for the script p, that is just a notation for a quantity called the electric dipole. This quantity is known as a vector, in which it has both a magnitude (length) and direction (angle). As such, we are often concerned with the scalar (magnitude) aspect of these vector quantities. So, the vertical lines surrounding the script p (|p|) indicate that we are looking for the magnitude (or size) of the electric dipole, not necessarily the direction that it is applied. This double vertical bar notation is also seen through math as an absolute value, meaning that we just want the length of the number from a set point (for example |-2| is two units away from zero). In the complex number work, we have a real part and imaginary part that can be thought of as a vector, so finding the magnitude of a complex number shows how far we are from the origin. This was a bit of a mini-lecture, so please let me know if I can help clarify anything above or add more context.

@@curiousaboutscience Thank you so much. The double vertical lines (double pipes) is only about the scalar part, and discards the other part (being a vector direction, a negative sign which in essence can be regarded as direction on the number line, or even the imaginary part of a complex number). That's what I understood from it.

@@SaeedNeamati Yes, I would add that this scalar part, magnitude (or length/distance) is easy to find in one dimension (number line) but would require the distance formula in the plane (complex or x-y) and higher dimensions. So, the directional parts of the vectors or imaginary parts of complex numbers aren't seen in this type of expression, but are needed via their components. What we say is that we take each component square it, add them together and then take the square root. For example: 1D: |-2|=√{(-2)²}=2 2D: Vector - a=<3,4>=3î+4ĵ=3x̂+4ŷ; |a|=√{3²+4²}=5 2D: Complex - x=3+4i; |x|=√{3²+4²}=5 or |x|=√{x*x}=√{(3-4i)(3+4i)}=√{3²+4²}=5

Whoever came up with this insight sure did save a lot of people a lot of times. Curiously, geometry is insanely insightful. This is absolutely a nice factoid from calculus and integrals of functions and coordinate systems. What was the last math class/topic you remember using?

@curiousaboutscience I've recently used binomial distribution to assess the company I work for revenue streams to identify and target key partners. I'm looking to learn more about derivatives and integrals as I think they can be key weapons in my arsenal as finance professional. I'm just fascinated by physics and maths in general though.

There are so many of these identities that come about at the most random of times in this book and another book by Jackson.

I will have to go back and look at the book and see when it is used explicitly. What I remember though is it is better to have these tools in the toolbox than not. haha

Thanks for watching! What a fun paper huh? Did you see Abbott's rebuttal?

This was such a clever way to find a path to the solution vs. the classical approach. The architects of this theory, and most theories, were truly artist that used mathematics and reason as their mediums. I am always impressed when I read their work!

So annoying at first, but they are so useful!

Thank you for watching! Happy learning! 🤓