The details of several steps in the particle-in a box middle inthis chapter have been omitted. Work out the details of thefollowing steps:
a.)Show that if Ψ =A sin rx + B cos sx (A, B, r, and s areconstants) 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 whenx=0 and x=a) require that r =± nπ/a, where n = any integer otherthan zero.
c.)Show that if r =±nπ/a, the energy levels of the particle aregiven 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 givesA=(2)1/2/a.
provide proper explanation for each and every part. lastexpert just copy and paste from book please do not copy ad pasteelaborate each and every step with explanation.
