Question

The details of several steps in the particle-in a box middle in this chapter have been omitted. Work out the details of the following steps:

a.)Show that if Ψ =A sin rx + B cos sx (A, B, r, and s are constants) is a solution to the wave equation for the one- dimensional box, then r = s = (2mE)1/2(2π/h)

b.)Show that if Ψ= A sin rx, the boundary conditions (Ψ =0 when x=0 and x=a) require that r =± nπ/a, where n = any integer other than zero.

c.)Show that if r =±nπ/a, the energy levels of the particle are given by E =n2h2/8ma2.

d.)Show that substituting the value of r given in part c into Ψ =A sin rx and applying the normalizing requirement gives A=(2)1/2/a.

provide proper explanation for each and every part. last expert just copy and paste from book please do not copy ad paste elaborate each and every step with explanation.

Answer 1