Consider an electron trapped in a 20 Å long box whose wavefunction is given by thefollowing linear combination of the particle's n= 2 and n = 3 states:.= ((x,tvי2nxsinV10´3x- sin4where E,a2ma²a. Determine if this wavefunction is properly normalized. If not, determine anappropriate value for a normalization constant.b. Show that this is not an eigenfunction to the PitB problem. What are the possibleresults that could be returned when the energy is measured and what are theprobabilities of measuring each of these results?c. Calculate Y(x,1) = ¥° (x,1)¥ (x.1) and sketch what this looks like for t=0,3th2xh,and 1(E,-E,)You will likely want2(E,- E.) (E,-E.)'to use a graphing program such as Excel, Mathematica, or Matlab for this. Whathappens to the most likely position to find the particle as time progresses? Does itmove? If so, with what frequency does it move?2(E, – E,)'

Given, ψ(x,t)=2a64sin2πxae-iE2th+104sin3πxae-iE3th ψ(x,t)=2a64|φ2>e-iE2th+104|φ3>e-iE3th a.…

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