Values of the agular momentum quantum number

1. Apr 18, 2007

fkliment2000

Hello!

Why is it the case, that the priciple quantum number limits the values of the angular momentum quantum number like

l <= n-1

How is it possible to derive this?

Thank you for your answers.

2. Apr 18, 2007

Hootenanny

Staff Emeritus
It falls out the the Schrodinger equation (SE) when solving the Hydrogen atom. On approach to solving the SE is to seperate the variables into different equations. In order to solve the SE, we seperate the radial part and set it equal to a constant. This yields what is known as the Colatitude equation. We then seperate the Azimuthal Equation (which coincidentaly is the easiest to solve) and solve. This gives the value of the constant in the Colatitude equation and the azimuthal quantum number. We then solve the Colatitude equation using ploynomial expansion and obtain solutions of the form $C = l(l+1)$ and the solution only exists if l = 0,1,2,3,...,n-1

More information is available at http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html#c2

3. Apr 19, 2007

fkliment2000

Thanks very much!!

4. Apr 19, 2007

masudr

Also, note that this restriction only holds for hydrogenic systems.

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