Problem 4.46 - QM in 3D Extras ⇢ Three-dimensional Harmonic Oscillator: Intro to Quantum Mechanics

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Why is the three-dimensional harmonic oscillator important in quantum mechanics? It serves as a model for real physical systems, approximating the behavior of atoms in a crystal lattice, molecular vibrations, and quantum dots. Its simplicity and solvability make it a valuable tool for understanding more complex interactions.

• 𝙿𝚛𝚘𝚋𝚕𝚎𝚖 𝙱𝚛𝚎𝚊𝚔𝚍𝚘𝚠𝚗 𝚃𝚒𝚖𝚎 𝚂𝚝𝚊𝚖𝚙𝚜:
00:00 - Background.
00:18 - Problem Statement.
02:22 - Part (a) - Separation of Variables.
10:00 - Part (b) - Degeneracy.
15:22 - Concluding Remarks.
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⍟ 𝐌𝐢𝐬𝐬𝐢𝐨𝐧 ⍟
Science is a phenomenal exploration of nature. We hope to hone our skills of problem solving by exposing ourselves to multiple contexts. In doing so, it can sometimes be challenging to see the connection between topics. I yearn to understand 𝙝𝙤𝙬 these aspects of physics, unite together. To accomplish this, I'll cover all of my old textbooks through QFT; the convergence point of the many modern scientists! These posts are very much in a "𝘯𝘰𝘵𝘦𝘴 𝘵𝘰 𝘴𝘦𝘭𝘧" style. 𝙈𝙮 𝙝𝙤𝙥𝙚 is that by sharing this exploration, I can help others navigate the beautiful world of mathematics & physics through problems and examples, connecting the mathematical tools to their physical ramifications.

#Curiousaboutscience

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⍟ 𝐂𝐫𝐞𝐝𝐢𝐭𝐬 ⍟
◉ ☞📚📖📓= Griffiths, David J., and Darrell F. Schroeter. “Chapter 4 Quantum Mechanics in Three Dimensions.” 𝘐𝘯𝘵𝘳𝘰𝘥𝘶𝘤𝘵𝘪𝘰𝘯 𝘵𝘰 𝘘𝘶𝘢𝘯𝘵𝘶𝘮 𝘔𝘦𝘤𝘩𝘢𝘯𝘪𝘤𝘴, 3rd ed., Cambridge University Press, 2018, pp. 131–197.

◉ ☞ 🖼 📸 = http://tinyurl.com/4v9nef5k
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