Ψ(x,0)=A(2ζ^2-1)(1+ζ)exp(-ζ^2/2), where ζ =(mω/ħ)^1/2 x. a) Using Table 2.1 and the definition of the harmonic oscillator wave functions given in section 2.3.2, rewrite the wave function above as a linear combination of normalized eigenfunctions for this potential (as you did in problem 1). Then, determine A and state which energies can be measured and with what probabilities. b)Find and as functions of time Table 2.1 H0=1, H1=2ζ, H2=4ζ^2, H3=8ζ^3-12ζ,H4=16ζ^4-48ζ^3+12,H5=32ζ^5-160ζ^3+120ζ