Problem 7 Consider a rotor with moment of inertia is I, that rotates freely around the z-axis. Define o to be the variable Euler angle of the rotor in the z-y plane. (a) Find the energy eigenvalues and the corresponding normalized eigenfunctions. (b) At time t = 0, the rotor is described by a wavefunction V(6,t = 0) = Asin'o with A a constant. Find the wavefunction V(6, t) at time t>0. Hint: You may want to consider the classical Hamiltonian of an analog classical problem as illustrated in the figure.
Problem 7 Consider a rotor with moment of inertia is I, that rotates freely around the z-axis. Define o to be the variable Euler angle of the rotor in the z-y plane. (a) Find the energy eigenvalues and the corresponding normalized eigenfunctions. (b) At time t = 0, the rotor is described by a wavefunction V(6,t = 0) = Asin'o with A a constant. Find the wavefunction V(6, t) at time t>0. Hint: You may want to consider the classical Hamiltonian of an analog classical problem as illustrated in the figure.
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Transcribed Image Text:Problem 7
Consider a rotor with moment of inertia is I, that rotates freely around the z-axis. Define o
to be the variable Euler angle of the rotor in the r-y plane.
(a) Find the energy eigenvalues and the corresponding normalized eigenfunctions.
(b) At time t = 0, the rotor is described by a wavefunction
V(6,t = 0) = Asin²o
with A a constat. Find the wavefunction V(6, t) at time t > 0.
Hìnt: You may want to consider the classical Hamiltonian of an analog classical problem as
illustrated in the figure.
y
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