Chapter 7, Problem 1CQ

To determine

The definition of quantum number.

Explanation of Solution

A number which labels possible values of conserved physical quantities like momentum or energy is known as quantum number. For any system , thepossible quantum states of the system are labled by the quantum number.

Forexample, for hydrogen atom the quantum numbers are principal quantum $\text{n=1,2,3}\mathrm{.....}$ the angular momentum quantum number $\mathcal{l}$ such that the absolute value of the angular momentum of the electron in an allowed state is $L^2=\mathcal{l}\left(\mathcal{l}+1\right){\hslash }^2$ the azimuthal quantum number $m=0,\pm 1,\_$ such that the angular momemtum component along the z- axis is $m\hslash \text{ for }m=0,\pm 1,\_,$ and the spin quantum number $m_s$ that specifies up spin and down spin along z- axis.

Which quantum number apply is determined by solving the Schrodinger equation and applying appropiate boundary conditios, which typicaslly restrict the possible solutions to those with specific values for various quantum number labeling the solutions.