Question

A particle of mass m confined to a line of length L from z = 0 to z = L has energies: En = (n^2?^2?^2)/(2mL^2) where n is a positive integer and corresponding normalised eigenfunctions ?n: ?n = ?(2/L) sin(n?z/L). (a) If the particle is in the n = 2 state, evaluate the probability to find the particle between z = 0 and z = L/3. (b) At time t = 0, the wall located at z = L is suddenly pulled out to the position at z = 2L while the particle is in the ground state. This change occurs so rapidly that instantaneously the wavefunction does not change. Calculate the probability that the particle will be in the n = 2 state of the expanded line, for which the particle has the same energy as it had in the ground state. Use sin^2 ? = 1/2 (1 - cos 2?) to do the integrals.

          A particle of mass m confined to a line of length L from z = 0 to z = L
has energies:
En = (n^2?^2?^2)/(2mL^2)
where n is a positive integer and corresponding normalised eigenfunctions
?n:
?n = ?(2/L) sin(n?z/L).
(a) If the particle is in the n = 2 state, evaluate the probability to find
the particle between z = 0 and z = L/3.
(b) At time t = 0, the wall located at z = L is suddenly pulled out to
the position at z = 2L while the particle is in the ground state. This
change occurs so rapidly that instantaneously the wavefunction does
not change. Calculate the probability that the particle will be in the
n = 2 state of the expanded line, for which the particle has the same
energy as it had in the ground state.
Use sin^2 ? = 1/2 (1 - cos 2?) to do the integrals.

A particle of mass m confined to a line of length L from z = 0 to z = L
has energies:
En = (n^2?^2?^2)/(2mL^2)
where n is a positive integer and corresponding normalised eigenfunctions
?n:
?n = ?(2/L) sin(n?z/L).
(a) If the particle is in the n = 2 state, evaluate the probability to find
the particle between z = 0 and z = L/3.
(b) At time t = 0, the wall located at z = L is suddenly pulled out to
the position at z = 2L while the particle is in the ground state. This
change occurs so rapidly that instantaneously the wavefunction does
not change. Calculate the probability that the particle will be in the
n = 2 state of the expanded line, for which the particle has the same
energy as it had in the ground state.
Use sin^2 ? = 1/2 (1 - cos 2?) to do the integrals.

Added by Ivan D.

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