Question

Consider a particle confined in a 1D box of length L. The energy spacing between any two consequtive energy level is propotional to

Answer 1

Energy spectrum of particle in a 1D box:

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

Energy spacing:

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

Therefore, at large n, energy spacing between any two consequtive energy level is propotional to n