[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M79DCFJ7EDKEVC1J2FKHTEX5":3,"skill-same:01M79DCFJ7EDKEVC1J2FKHTEX5":59},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":16,"categories":17,"keywords":18,"publishedAt":19,"linkOnly":20,"markdownContent":21,"markdownBody":22,"frontMatter":23,"refName":29,"commitSha":30,"skillDirectory":31,"forksCount":32,"repositoryHtmlUrl":33,"repositoryHomepageUrl":34,"ownerHtmlUrl":35,"ownerBlogUrl":36,"ownerDescription":37,"updatedAt":38,"install":39,"resources":52},"01M79DCFJ7EDKEVC1J2FKHTEX5","finite-square-well-bound-states",null,"Finite Square Well and Bound States in Quantum Mechanics (Schrödinger). Theoretical foundations, governing equations, analytical problem-solving methods, and typical archetypes.","hamzabellouch\u002Fagent-skills","hamzabellouch","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F237856042?v=4","01M79BRYW7XAMK3YDWQEMTWGWS","Hamza Bellouch","01M79BRYWXQV3JK2TGVTX8GN2A",8,"MIT","https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FPhysics\u002FQuantum_Physics_and_Simulation\u002Ffinite-square-well-bound-states\u002FSKILL.md",[],[],"2026-11-15 14:19:17",false,"---\nname: finite-square-well-bound-states\ndescription: Finite Square Well and Bound States in Quantum Mechanics (Schrödinger). Theoretical foundations, governing equations, analytical problem-solving methods, and typical archetypes.\nmetadata:\n  id: qm.schrodinger.finite_well\n  domain: Quantum Mechanics\n  subdomain: Schrödinger\n  difficulty: 4\u002F5\n---\n\n# Finite Square Well and Bound States\n\n**ID:** `qm.schrodinger.finite_well`  \n**Domain:** Quantum Mechanics → Schrödinger  \n**Difficulty:** 4\u002F5\n\n## Prerequisites\n- qm.schrodinger.particle_in_box\n\n## Core Concepts\n- finite well\n- evanescent tails\n- bound vs scattering states\n- transcendental eigenvalue equation\n\n## Key Equations\n$$\n\\tan(ka) = \\frac{\\kappa}{k}\\ \\text{(even)}\n$$\n$$\nk^2 + \\kappa^2 = \\frac{2mV_0}{\\hbar^2}\n$$\n\n## Methods\n- Solve matching conditions at the walls\n- Solve the transcendental equation graphically\u002Fnumerically\n- Identify the number of bound states from V_0 a^2\n\n## Typical Problem Types\n- Number of bound states in a well\n- Penetration depth of the tail\n- Deuteron as a shallow bound state\n\n## Common Pitfalls\n- Assuming infinite-well wavefunctions\n- Forgetting the exponentially decaying tail\n\n## Related Skills\n- qm.schrodinger.tunneling\n- qm.approx.wkb\n\n## References\n- Griffiths QM Ch.2\n- Cohen-Tannoudji Ch.2\n","# Finite Square Well and Bound States\n\n**ID:** `qm.schrodinger.finite_well`  \n**Domain:** Quantum Mechanics → Schrödinger  \n**Difficulty:** 4\u002F5\n\n## Prerequisites\n- qm.schrodinger.particle_in_box\n\n## Core Concepts\n- finite well\n- evanescent tails\n- bound vs scattering states\n- transcendental eigenvalue equation\n\n## Key Equations\n$$\n\\tan(ka) = \\frac{\\kappa}{k}\\ \\text{(even)}\n$$\n$$\nk^2 + \\kappa^2 = \\frac{2mV_0}{\\hbar^2}\n$$\n\n## Methods\n- Solve matching conditions at the walls\n- Solve the transcendental equation graphically\u002Fnumerically\n- Identify the number of bound states from V_0 a^2\n\n## Typical Problem Types\n- Number of bound states in a well\n- Penetration depth of the tail\n- Deuteron as a shallow bound state\n\n## Common Pitfalls\n- Assuming infinite-well wavefunctions\n- Forgetting the exponentially decaying tail\n\n## Related Skills\n- qm.schrodinger.tunneling\n- qm.approx.wkb\n\n## References\n- Griffiths QM Ch.2\n- Cohen-Tannoudji Ch.2\n",{"name":5,"metadata":24,"description":7},{"id":25,"domain":26,"subdomain":27,"difficulty":28},"qm.schrodinger.finite_well","Quantum Mechanics","Schrödinger","4\u002F5","main","e905af21e5f1e1c3ca605e9656c3a7930360a84e","Physics\u002FQuantum_Physics_and_Simulation\u002Ffinite-square-well-bound-states",1,"https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills","https:\u002F\u002Fhamzabellouch.github.io\u002F","https:\u002F\u002Fgithub.com\u002Fhamzabellouch","hamzabellouch.github.io","CEO & Founder of @tknoglobal | Researcher in Technology & Applied Sciences.","2026-10-17 03:20:19",{"source":8,"skillName":5,"commands":40,"prompt":50,"zipAvailable":51},[41,44,47],{"tool":42,"command":43},"npx","npx skills add hamzabellouch\u002Fagent-skills --skill finite-square-well-bound-states",{"tool":45,"command":46},"bunx","bunx skills add hamzabellouch\u002Fagent-skills --skill finite-square-well-bound-states",{"tool":48,"command":49},"pnpm","pnpm dlx skills add hamzabellouch\u002Fagent-skills --skill finite-square-well-bound-states","安装技能，技能地址：https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FPhysics\u002FQuantum_Physics_and_Simulation\u002Ffinite-square-well-bound-states\u002FSKILL.md",true,[53],{"path":54,"resourceType":55,"resourceTypeDesc":56,"sizeBytes":57,"sourceHtmlUrl":58},"metadata.json","REFERENCE","参考文档",1141,"https:\u002F\u002Fgithub.com\u002Fhamzabellouch\u002Fagent-skills\u002Fblob\u002Fmain\u002FPhysics\u002FQuantum_Physics_and_Simulation\u002Ffinite-square-well-bound-states\u002Fmetadata.json",[60,67,74,81,88,95],{"skillNo":61,"name":62,"nameZh":6,"description":63,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":64,"categories":65,"keywords":66,"publishedAt":19},"01M79FHH2H815A9TAP6WNKH4Q8","security-audit","Comprehensive security guidance, source code audit, vulnerability assessment, and penetration test review for codebases, APIs, microservices, CLI tools, libraries, and LLM-backed applications. 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