Problem 10.5 - Phase Shifts ⇢ Potential Well & Barrier: Intro to Quantum Mechanics

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Imagine a particle traveling toward a mysterious quantum potential well—how does it respond? Does it pass through, or is it forced to reflect? In this fascinating problem, we dive into the strange world of quantum mechanics to explore how a particle’s wave function reflects off a potential well, and what happens when it encounters an impenetrable barrier. Along the way, we’ll uncover how the phase shift reveals key insights about the particle’s behavior, and why this technique is so important for understanding quantum systems. Ready to unravel the quantum puzzle? Let’s get started!

• 𝙿𝚛𝚘𝚋𝚕𝚎𝚖 𝙱𝚛𝚎𝚊𝚔𝚍𝚘𝚠𝚗 𝚃𝚒𝚖𝚎 𝚂𝚝𝚊𝚖𝚙𝚜:
00:00 - Intro & Problem Statement.
01:11 - Background.
02:16 - Part (a): Finding the Reflected Wave 𝜓ᵣ.
10:01 - Part (b): Amplitude Checks |𝘈|² = |𝘉|².
12:12 - Part (c): Phase Shifts δ.
15:56 - Concluding Remarks.
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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 5 Identical Particles.” 𝘐𝘯𝘵𝘳𝘰𝘥𝘶𝘤𝘵𝘪𝘰𝘯 𝘵𝘰 𝘘𝘶𝘢𝘯𝘵𝘶𝘮 𝘔𝘦𝘤𝘩𝘢𝘯𝘪𝘤𝘴, 3rd ed., Cambridge University Press, 2018, pp. 198–231.

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