A quantum mechanical particle is confined to a one-dimensional infinite potential welldescribed by the function V(x) = 0 in the region 0 < x < L, V(x) = ∞ elsewhere.The normalised eigenfunctions for a particle moving in this potential are:Yn(x)=√2Nπsin -XL Lwhere n = 1, 2, 3, ..a) Write down the expression for the corresponding probability density function. Sketchthe shape of this function for a particle in the ground state (n = 1).b) Annotate your sketch to show the probability density function for a classical particlemoving at constant speed in the well. Give a short justification for the shape of yoursketch.c) Briefly describe, with the aid of a sketch or otherwise, the way in which the quantumand the classical probability density functions are consistent with the correspondenceprinciple for large values of n.

Step 1: Given: Particle in a 1-D infinite potential well described by the potential:V(x) =0,…

A quantum mechanical particle is confined to a one-dimensional infinite potential well described by the function V(x) = 0 in the region 0 < x < L, V(x) = ∞ elsewhere. The normalised eigenfunctions for a particle moving in this potential are: Yn(x) = = NTT sin -X Vī L where n = 1, 2, 3, ... a) Write down the expression for the corresponding probability density function. Sketch the shape of this function for a particle in the ground state (n = 1).

A quantum mechanical particle is confined to a one-dimensional infinite potential well described by the function V(x) = 0 in the region 0 < x < L, V(x) = ∞ elsewhere. The normalised eigenfunctions for a particle moving in this potential are: Yn(x) = = NTT sin -X Vī L where n = 1, 2, 3, ... a) Write down the expression for the corresponding probability density function. Sketch the shape of this function for a particle in the ground state (n = 1).