Why Does the Hydrogen-Atom Wave Function Equal R(r)cita(cita)phi(phi)?

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Homework Help Overview

The discussion revolves around the wave function of the hydrogen atom and its representation as a product of functions R(r), Θ(θ), and Φ(φ). Participants explore the underlying reasons for this representation in the context of the Schrödinger equation.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants discuss the separability of the Schrödinger equation and how it leads to the wave function's form. Others question the assumptions about the equation's structure before solving it.

Discussion Status

The discussion is active, with participants providing insights into the nature of separable equations and the implications for the hydrogen atom's wave function. There is no explicit consensus, but various interpretations and clarifications are being explored.

Contextual Notes

Participants note that the representation of the wave function is not immediately apparent and relies on the characteristics of the differential equations involved.

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why does it equal R(r)cita(cita)phi(phi)?
 
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Beforehand there is nothing that tells you it does before you solve the Shrodinger equation. It is just lucky that the problem falls into the class of differential equations known as "seperable equations". You know that it does equal [itex]R(r)\Theta (\theta) \Phi (\phi)[/itex] because it ends up working in the equation.
 
Because the Schrödinger equation for the hydrogen atom (a partial differential equation in the three variables [itex]r, \theta, \phi[/itex] is separable into three ordinary differential equations, one for each variable.
 
thank you very much!
 

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