Problem 10.7 - Phase Shift Analysis ⇢ S-Wave Scattering from a δ Shell: Intro to Quantum Mechanics

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Have you ever wondered what happens when a quantum particle encounters a shell of pure potential? In this intriguing problem, we explore how even the thinnest barrier can dramatically shift a particle's wavefunction. What exactly is a delta-function shell, and why does it cause such a fascinating effect? Join me as we unravel the mysteries of quantum scattering, where the tiniest forces lead to big changes! Prepare to see how the S-wave phase shift reveals the hidden influence of this almost invisible potential. Ready to find out why this is so important in quantum mechanics?

• 𝙿𝚛𝚘𝚋𝚕𝚎𝚖 𝙱𝚛𝚎𝚊𝚔𝚍𝚘𝚠𝚗 𝚃𝚒𝚖𝚎 𝚂𝚝𝚊𝚖𝚙𝚜:
00:00 - Intro & Problem Statement.
01:21 - Background.
02:53 - Stop 1: Forming the Wavefunction 𝘶(𝘳).
07:00 - Stop 2: Applying the Boundary Conditions.
11:58 - Stop 3: Phase Shift 𝛿₀.
18:44 - 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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◉ ☞📚📖📓= Griffiths, David J., and Darrell F. Schroeter. “Chapter 10 Scattering.” 𝘐𝘯𝘵𝘳𝘰𝘥𝘶𝘤𝘵𝘪𝘰𝘯 𝘵𝘰 𝘘𝘶𝘢𝘯𝘵𝘶𝘮 𝘔𝘦𝘤𝘩𝘢𝘯𝘪𝘤𝘴, 3rd ed., Cambridge University Press, 2018, pp. 376–401.

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