Question

Recognize how quantum numbers arise as a consequence of the wave model.

Explain it

Answer 1

Quantum numbers arise in the process of solving the Schrodinger equation by constraints or boundary conditions which must be applied to get the solution to fit the physical situation.

The case of a particle confined in a one-dimensional box can be used to show how quantum numbers arise.Foundational to this process is the nature of the quantum mechanical wavefunction and its root in probability. For a particle in space, the wavefunction can be written

This wavefunction is subject to the constraints

In this process, we see that the quantum number n arises from the nature of the wavefunction and its solution when it is forced to fit the boundary conditions imposed by the potential.