2. Consider a particle of mass m moving along a circle of radius R and subject to a periodic potential field V(0+2) = V(0) for 0 ≤ 0 ≤ 27, with being the polar angle of the particle position. Its wavefunction at the initial time to is given by o(0). (2.1) What is the Hamiltonian Ĥ of this particle? (2.2) When the particle is free, i.e., V(0) = 0 V0, show that the eigenvalues of Ĥ are discrete. (23) When Y(9) # 0, find the wave function (e,t) at the time t > to using the path integral representation.
2. Consider a particle of mass m moving along a circle of radius R and subject to a periodic potential field V(0+2) = V(0) for 0 ≤ 0 ≤ 27, with being the polar angle of the particle position. Its wavefunction at the initial time to is given by o(0). (2.1) What is the Hamiltonian Ĥ of this particle? (2.2) When the particle is free, i.e., V(0) = 0 V0, show that the eigenvalues of Ĥ are discrete. (23) When Y(9) # 0, find the wave function (e,t) at the time t > to using the path integral representation.
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Transcribed Image Text:2. Consider a particle of mass m moving along a circle of radius R and subject to a periodic potential field
V (9 + 27) = V (8) for 0 < 0 < 27, with 0 being the polar angle of the particle position. Its wavefunction at the initial
tìme to is given by vo(0).
(2.1) What is the Hamiltonian Ĥ of this particle?
(2.2) When the particle is free, i.e., V(0) = 0 show that the eigenvalues of H are discrete.
(? 3) When Y(0) 0, find the wave function V(0,t) at the time t > to using the path integral representation.
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