Consider an electron trapped in a 20 Å long box whose wavefunction is given by the following linear combination of the particle's n = 2 and n = 3 states: Y(x,t) =, 2nx -sin V10 sin where E, 2ma? a. Determine if this wavefunction is properly normalized. If not, determine an appropriate value for a normalization constant.
Consider an electron trapped in a 20 Å long box whose wavefunction is given by the following linear combination of the particle's n = 2 and n = 3 states: Y(x,t) =, 2nx -sin V10 sin where E, 2ma? a. Determine if this wavefunction is properly normalized. If not, determine an appropriate value for a normalization constant.
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Transcribed Image Text:Consider an electron trapped in a 20 Å long box whose wavefunction is given by the
following linear combination of the particle's n= 2 and n = 3 states:
.= ((x,tvי
2nx
sin
V10
´3x
- sin
4
where E,
a
2ma²
a. Determine if this wavefunction is properly normalized. If not, determine an
appropriate value for a normalization constant.
b. Show that this is not an eigenfunction to the PitB problem. What are the possible
results that could be returned when the energy is measured and what are the
probabilities of measuring each of these results?
c. Calculate Y(x,1) = ¥° (x,1)¥ (x.1) and sketch what this looks like for t=0,
3th
2xh
,and 1
(E,-E,)
You will likely want
2(E,- E.) (E,-E.)'
to use a graphing program such as Excel, Mathematica, or Matlab for this. What
happens to the most likely position to find the particle as time progresses? Does it
move? If so, with what frequency does it move?
2(E, – E,)'
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