Problem 6.79

Demonstrate that the wave functions of the stationary states of a particle confined in a unidimensional potential well with infinitely high walls are orthogonal, i.e. they satisfy the condition \(\int_{0}^{l} \psi_{n} \psi_{n}^{\prime} d x=0\) if \(n^{\prime} \neq n .\) Here \(l\) is the width of the well, \(n\) are integers.