The Hydrogen Atom

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Hydrogen Schrodinger Equation

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Quantum Numbers from Hydrogen EquationsThe hydrogen atom solution requires finding solutions to the separated equations which obey the constraints on the wavefunction. The solution to the radial equation can exist only when a constant which arises in the solution is restricted to integer values. This gives the principal quantum number:
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Separating the Hydrogen EquationOne of the approaches to solving a partial differential equation is to separate it into individual equations for each variable involved. The hydrogen Schrodinger equation is separable, and collecting all the radiusdependent terms and setting them equal to a constant gives the radial equation: Then the angular parts of the equation can be separated into a colatitude equation: and an azimuthal equation. 
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