Problem 6.15/6.16 - Rotation Operator ⇢ Scalar & Vector Transformations: Intro to Quantum Mechanics скачать в хорошем качестве

Problem 6.15/6.16 - Rotation Operator ⇢ Scalar & Vector Transformations: Intro to Quantum Mechanics

⍟ 𝐏𝐃𝐅 ➜ https://tinyurl.com/3rf6k7mf 𝐃𝐨𝐧𝐚𝐭𝐞 ➜ https://buymeacoffee.com/curiousabout... 𝐂𝐡𝐚𝐩𝐭𝐞𝐫 𝐍𝐨𝐭𝐞𝐬 ➜ https://tinyurl.com/47d6jp55 ⍟ ---------------------------------------------------- ⍟ 𝐀𝐛𝐨𝐮𝐭 𝐓𝐡𝐢𝐬 𝐕𝐢𝐝𝐞𝐨 ⍟ Quantum mechanics heavily relies on symmetry principles, with rotational symmetry being particularly fundamental. This symmetry simplifies the mathematical treatment of physical problems and aids in formulating conservation laws. Specifically, the invariance of a system under rotation leads to the conservation of angular momentum, as explained by Noether's theorem, which states that every continuous symmetry corresponds to a conserved quantity. The study of transformations under rotations is closely related to the representation theory of groups, particularly the rotation group 𝘚𝘖(3) and its quantum counterpart, 𝘚𝘜(2). This mathematical framework underpins much of quantum mechanics, including particle classification and spin behavior. Spin and orbital angular momentum concepts are central to understanding atomic structures, electron behavior in magnetic fields, and fundamental particle properties. Operators' transformation properties under rotations help derive selection rules for transitions between quantum states, determining which transitions are allowed or forbidden in processes like electromagnetic radiation absorption and emission. In summary, the invariance of scalars under rotation and the transformation of vectors are foundational concepts in quantum mechanics. These principles ensure the consistency, predictability, and physical relevance of quantum mechanical models, underpinning much of the theory's structure and application. 𝙋𝙞𝙘𝙩𝙪𝙧𝙚 𝙍𝙚𝙛𝙚𝙧𝙚𝙣𝙘𝙚: • https://math.stackexchange.com/questi... • 𝙿𝚛𝚘𝚋𝚕𝚎𝚖 𝙱𝚛𝚎𝚊𝚔𝚍𝚘𝚠𝚗 𝚃𝚒𝚖𝚎 𝚂𝚝𝚊𝚖𝚙𝚜: 00:00 - Background. 00:27 - Problem Statement. 01:34 - Prob 6.14 ↦ https://tinyurl.com/ypzb2rhs 03:37 - Stop 1: Problem 6.15 - Scalars. 08:47 - Stop 2: Problem 6.16 - Vectors. 16:51 - Concluding Remarks. ---------------------------------------------------- ⍟ 𝐒𝐮𝐩𝐩𝐨𝐫𝐭 𝐓𝐡𝐢𝐬 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 ⍟ • ▶️ 𝘚𝘶𝘣𝘴𝘤𝘳𝘪𝘣𝘦 ▶️ ➜ http://tinyurl.com/4kd8wahb • 🔎 𝘗𝘢𝘵𝘳𝘦𝘰𝘯 🔍 ➜   / curiousaboutscience   • ☕ Buy Me a Coffee ☕ ➜ https://buymeacoffee.com/curiousabout... • 📖 𝘈𝘮𝘢𝘻𝘰𝘯 𝘉𝘰𝘰𝘬 𝘓𝘪𝘯𝘬𝘴 📖 ↳ QM ➜ https://amzn.to/48Xu8mx ↳ EM ➜ https://amzn.to/3TYJ8MN • ⚙️ 𝘈𝘮𝘢𝘻𝘰𝘯 𝘎𝘦𝘢𝘳 𝘓𝘪𝘯𝘬𝘴 ⚙️ ↳ 💻 ➜ https://amzn.to/3OZ5lqR ↳ 🎙️ ➜ https://amzn.to/49ryumD ---------------------------------------------------- ⍟ 𝐋𝐞𝐭'𝐬 𝐂𝐨𝐧𝐧𝐞𝐜𝐭! ⍟ • 𝘐𝘯𝘴𝘵𝘢𝘨𝘳𝘢𝘮 ➜   / curiousaboutscience   • 𝘛𝘸𝘪𝘵𝘵𝘦𝘳/𝕏 ➜   / sciencenerd_cas   ---------------------------------------------------- ⍟ 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 • Stay Curious & Happy Learning! ⇢ Share knowledge - tag a friend! ⇢ Subscribe for more! ⇢ Don't forget to turn on video notifications! ---------------------------------------------------- ⍟ 𝐂𝐫𝐞𝐝𝐢𝐭𝐬 ⍟ ◉ ☞📚📖📓= Griffiths, David J., and Darrell F. Schroeter. “Chapter 6 Symmetries & Conservation Laws.” 𝘐𝘯𝘵𝘳𝘰𝘥𝘶𝘤𝘵𝘪𝘰𝘯 𝘵𝘰 𝘘𝘶𝘢𝘯𝘵𝘶𝘮 𝘔𝘦𝘤𝘩𝘢𝘯𝘪𝘤𝘴, 3rd ed., Cambridge University Press, 2018, pp. 232–275. ◉ ☞ 🖼 📸 = http://tinyurl.com/4v9nef5k ----------------------------------------------------