Problem 4.15 - Hydrogen Atom ⇢ Expectation Values of Ground State: Introduction to Quantum Mechanics

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Dive into the fascinating realm of hydrogen atoms, focusing specifically on the ground state of its electron and spatial expectation values and more.

• 𝙿𝚛𝚘𝚋𝚕𝚎𝚖 𝙱𝚛𝚎𝚊𝚔𝚍𝚘𝚠𝚗 𝚃𝚒𝚖𝚎 𝚂𝚝𝚊𝚖𝚙𝚜:
0:00 - Background.
0:50 - Problem Statement.
1:40 - Start of Solution - Setup.
2:55 - Part (a) Constructing 𝜓₁₀₀(𝘳, 𝜃, 𝜙).
7:14 - Part (a) Expectation Values up to ⟨𝘳⟩ & ⟨𝘳²⟩.
11:50 - Part (b) Expectation Values ⟨𝘹⟩ and ⟨𝘹²⟩ for 𝜓₁₀₀.
14:51 - Part (c) ⟨𝘹²⟩ for 𝜓₂₁₁. Note ↦    • Problem 4.13 - Hydrogen Atom ⇢ Spatial Wav...  
18:49 - 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.

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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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