Question

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

Answer 1

Since energy is at the level n $E_n = \frac {h^{2}n^{2}}{8ml^{2}}$

then the energy difference $\Delta E_n = E_{n+1} - E_n = \frac{h^{2}(2n+1)}{8ml^{2}}$