Problem 2. An electron moves in the presence of a uniform magnetic field in the z direction, as above. a. Evaluate II, II, where e А, eAy Py Ily (2) Ра с с b. By comparing the Hamiltonian and the commutation relation obtained in (a) with those of the one-dimensional oscillator problem, show how we can immediately write the energy eigenvalues as h2k2 leBh 1 Ek.n (3) 2m тс where hk is a continuous eigenvalue of the p2 operator and n is a nonnegative integer including zero. Give a physical interpretation of the frequency of the harmonic oscillator
Problem 2. An electron moves in the presence of a uniform magnetic field in the z direction, as above. a. Evaluate II, II, where e А, eAy Py Ily (2) Ра с с b. By comparing the Hamiltonian and the commutation relation obtained in (a) with those of the one-dimensional oscillator problem, show how we can immediately write the energy eigenvalues as h2k2 leBh 1 Ek.n (3) 2m тс where hk is a continuous eigenvalue of the p2 operator and n is a nonnegative integer including zero. Give a physical interpretation of the frequency of the harmonic oscillator
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Transcribed Image Text:Problem 2. An electron moves in the presence of a uniform magnetic field in the z direction, as
above.
a. Evaluate II, II, where
e А,
eAy
Py
Ily
(2)
Ра
с
с
b. By comparing the Hamiltonian and the commutation relation obtained in (a) with those of the
one-dimensional oscillator problem, show how we can immediately write the energy eigenvalues as
h2k2
leBh
1
Ek.n
(3)
2m
тс
where hk is a continuous eigenvalue of the p2 operator and n is a nonnegative integer including zero.
Give a physical interpretation of the frequency of the harmonic oscillator
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