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Q4.1 Determine explicitly (i.e. give all the details of the derivation), the energy eigenvalues En and the normalised energy eigenfunctions {øn (x)} for a particle moving in a one dimensional 'box' where the potential energy is U (x) = 0 for 0 < x < a, U (x) = o for x < 0 or x > a. Show that the average or mean value for the position r of a particle in a state represented by the nth eigenfunction is a If the particle's wavefunction is represented by the eigenfunction o, (x), find an integral expression for the probability of finding the particle somewhere in the interval b

Q4.1 Determine explicitly (i.e. give all the details of the derivation), the energy eigenvalues En and the normalised energy eigenfunctions {øn (x)} for a particle moving in a one dimensional 'box' where the potential energy is U (x) = 0 for 0 < x < a, U (x) = o for x < 0 or x > a. Show that the average or mean value for the position r of a particle in a state represented by the nth eigenfunction is a If the particle's wavefunction is represented by the eigenfunction o, (x), find an integral expression for the probability of finding the particle somewhere in the interval b

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Q4.1 Determine explicitly (i.e. give all the details of the derivation), the energy eigenvalues En and the normalised energy eigenfunctions {øn (x)} for a particle moving in a one dimensional 'box' where the potential energy is U (x) = 0 for 0 <x<a, U (x) = o for x <0 or x > a. Show that the average or mean value for the position x of a particle in a state represented by the nth eigenfunction is a If the particle's wavefunction is represented by the eigenfunction ø, (x), find an integral expression for the probability of finding the particle somewhere in the interval b <x <cwhere 0 < b < c < a.
Transcribed Image Text:Q4.1 Determine explicitly (i.e. give all the details of the derivation), the energy eigenvalues En and the normalised energy eigenfunctions {øn (x)} for a particle moving in a one dimensional 'box' where the potential energy is U (x) = 0 for 0 <x<a, U (x) = o for x <0 or x > a. Show that the average or mean value for the position x of a particle in a state represented by the nth eigenfunction is a If the particle's wavefunction is represented by the eigenfunction ø, (x), find an integral expression for the probability of finding the particle somewhere in the interval b <x <cwhere 0 < b < c < a.
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