Quantum Chemistry/Example 2

Question Starting with the wave equation of a 1D box: The classical probability of a particle existing in the region of the box [0, 1/L] is, Where is the length of the 1D box, is the principle quantum number, and is the position of the particle in a 1D box. Derive an equation that calculates the probability of the particle being in the [0, 1/L] for the quantum mechanical particle in a 1D box. Is this result compatible with the correspondence principle? Solution