Uses of Laguerre Differential Equ.

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SUMMARY

The Laguerre Differential Equation is crucial in solving Schrödinger's Equation, particularly for determining the quantum-mechanical wave function of hydrogen. It specifically pertains to the radial component of the wave function. The discussion highlights the connection between the Laguerre Differential Equation and Laguerre polynomials, which are integral to the solution process. Resources that provide detailed explanations of these concepts are recommended for further understanding.

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  • Understanding of Schrödinger's Equation
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  • Knowledge of differential equations
  • Basic concepts of wave functions
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  • Research the application of Laguerre polynomials in quantum mechanics
  • Study the radial wave functions in hydrogen atom models
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Students and professionals in physics, particularly those focusing on quantum mechanics, as well as mathematicians interested in differential equations and their applications in physical theories.

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Does anybody know what the use of the Laguerre Differential Equation would be? I am having a hard time finding what areas of physics this diff. eq. is used in. Thanks.
 
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It arises in solving Schrödinger's Equation to find the quantum-mechanical wave function of hydrogen. Specifically, it's associated with the radial part of the wave function. See this site, for example.

(Hmm, I see it doesn't mention Laguerre's equation specifically by name, but it does come up with the Laguerre polynomials which are part of the solution.)
 
Thanks

Thank you, that site looks like it will help out quite a bit. It looks like it give a much more detail explanation that a lot of the other site I have seen.
 

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