Question

find a general equation for energy difference between two consecutive
state for a particle confined within a potential width of a

Answer 1

Energy levels in infinite potential well:

$$E_n =\frac{n^2 \pi^2 \hbar^2}{2 m a^2}$$

where n is a positive integer (1,2,3,4...) .

Therefore, energy difference between two consecutive

state

$$\Delta_n = E_{n+1}-E_n =\frac{(2n+1) \pi^2 \hbar^2}{2 m a^2}$$