Physics · Quantum Mechanics

A quantum mechanical particle of mass m is confined in a one-dimensional infinite potential well whose walls are located at x = 0 and x = 1. The wave function of the particle inside the well is ψ(x) = N[x ln(x) + (1-x) ln(1-x)] for some normalization constant N. An experimentalist measures the position of the particle on a large ensemble. The mean of the outcomes (expectation value ⟨x⟩) is found to be 1/n, where n is an integer. What is n?