Quantum Numbers

Quantum Number

Principal Quantum Number

$$ \large n = 0, 1, 2, 3, ... $$

Orbital Quantum Number

$$ \large l = 0, 1, 2, ... ,n-1 $$

Magnetic Quantum Number

$$ \large m = -l, -l+1, ..., -1, 0, 1, ... l-1, l $$

In total, there are $2l+1$ numbers.

  • GRE Physics GR0877 Problem 064

Spin Quantum Number

$$ \large m_s = +\frac{1}{2}, -\frac{1}{2} $$

Orbital Angular Momentum

$$ \large L = \sqrt{l(l+1)}\hbar $$$$ \large L^2 = l(l+1)\hbar^2 $$$$ \large L_z = m\hbar $$
  • GRE Physics GR0177 Problem 081

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