Quantum Number

The 3 quantum numbers:

• $n$ is the principal quantum number
• $l$ is the ortbial angular momentum quantum number
• $m_l$ is the magnetic (azimuthal) quantum number The constraints of the quantum numbers are as follows:

$$n,l,m_l\in \mathbb{Z}n>0l<n|m_l|\le l$$

• Total number of states is $n^2$
• Higher values of $n$ correspond to higher orbits from the nucleus, by a factor of $n$
• $E_n=-\frac{E_0}{n^2}$, $E_0=\frac{{\hslash }^2}{2\mu a_0^2}$
• Energy only depends on $n$, therefore $l$ and $m_l$ can vary while maintaining a constant energy. This means there are a lot of degenerate states!

Also Strangeness Also Charm

NL Shorthand

Orbital Angular Momentum Quantum Number $l$
$l$	0	1	2	3	4	5	6	7	8
Letter	s	p	d	f	g	h	a	b	c
A state with $n=2,l=1$ is called a $2p$ state