I really need a resource to explain the linear potential well to me

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SUMMARY

The discussion centers on the challenges faced by learners trying to understand the linear potential well in quantum mechanics. The user expresses frustration over resources that inadequately explain the transition from the potential well to the differential equation involving the Airy equation. They seek comprehensive tutorials or videos that detail each step of the process, particularly how to derive energy eigenvalues from the Airy equation. The lack of accessible educational content on this fundamental topic is highlighted as a significant barrier to understanding.

PREREQUISITES
  • Understanding of quantum mechanics fundamentals
  • Familiarity with differential equations
  • Knowledge of the Airy equation and its applications
  • Basic concepts of energy eigenvalues in quantum systems
NEXT STEPS
  • Research comprehensive tutorials on the linear potential well in quantum mechanics
  • Explore resources explaining the derivation of the Airy equation
  • Study the process of finding energy eigenvalues from differential equations
  • Look for video lectures specifically addressing the linear potential well and its solutions
USEFUL FOR

Students of quantum mechanics, educators seeking teaching resources, and anyone struggling with the mathematical foundations of the linear potential well.

richyw
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So I am trying to learn this. It is not making sense to me. Every single resource I have found tells me I need to make some weird substitution, and then it becomes a differential equation that has the Airy equation as a solution, and then skips to finding the energy eigenvalues as a function of the roots of the Airy equation.

Everything is skipping steps and I honestly can't see what is going on. Does anyone know of a video that explains this? Or a resource that shows EVERY step. I'm pulling my hair out over this one. My textbook kindly gave me a picture of the solutions, with not mention at all on how to solve it. Youtube seems to be devoid of videos. It seems crazy to me that no one has made a video on like the first potential we ever learn about in physics...
 
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