RE: LeoThread 2026-03-13 16-36

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Spherical Harmonics in Atomic Orbitals and Magnetic Fields

#math #sphericalharmonics #calculus #atomicphysics #magnet

leofinance
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In this video, I go over an overview of how spherical harmonics show up in the equations for atomic orbitals and magnetic fields. The Schrödinger equation is a partial differential equation that governs the wave function that mathematically describes a quantum state. Solutions to the Schrödinger equation are standing waves called stationary states or energy eigenstates or "atomic orbitals". I go over the Schrödinger equation for the electron in a hydrogen atom, which is also applicable to hydrogen-like atoms (any atom or ion with a single electron), and the corresponding solution that involves spherical harmonics. Similarly, I show that the spherical harmonics arise also in the equation of magnetic fields, which are derived from the mathematical scalar potential function.

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Here is what this big science poster is showing:

  1. The Blurry, Glowing Pictures

Imagine you put a super-fast, glowing firefly inside a jar in a dark room and took a blurry photo of it zooming around. That firefly is an electron (a tiny, invisible piece of an atom). The bright, glowing spots in those black squares are like a map showing where the electron spends the most time buzzing around.

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  1. The Balloon Shapes (Blue, Yellow, and Rainbow)

Electrons don't fly in flat circles like racecars on a track. They zoom around the center of the atom in really funky 3D shapes!

Some of their paths look like round balls.

Some look like two balloons tied together.

Some even look like four-leaf clovers or donuts!

Scientists call these shapes "orbitals," which is just a fancy word for the electron's neighborhood.

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Thanks for the insights, good sir!

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Thanks for the spark! Led to a cool back-n-forth w/ AI that gave me a better understanding of quantum concepts.

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  1. The Math and Secret Codes

All those confusing letters and numbers (like the "Schrödinger equation" at the bottom left) are the secret math rules that tell the electron how to move. It is like a super complicated recipe that scientists use to draw those firefly maps.

  1. The Scribbly Magnet Box

That box in the top right with the blue and red scribbles is showing the invisible force field around a magnet. It shows how the invisible pulling energy flows out of one end of a magnet and loops back into the other end.

So, what is the whole picture?
It’s a big cheat sheet showing what the invisible, tiny world inside an atom looks like.

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