Consider the Hamiltonian describing an electron in an external electric field E 1 -p² – eƐx 2m H = (a) Use the commutation relations between the operators x and p to obtain the equations of motion describing the time-dependence of (x) and (p). (b) Solve the equations of motion from (a) above and express the solutions in terms of initial values of x and p, i.e. x(0) and p(0)t.
Consider the Hamiltonian describing an electron in an external electric field E 1 -p² – eƐx 2m H = (a) Use the commutation relations between the operators x and p to obtain the equations of motion describing the time-dependence of (x) and (p). (b) Solve the equations of motion from (a) above and express the solutions in terms of initial values of x and p, i.e. x(0) and p(0)t.
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Transcribed Image Text:Consider the Hamiltonian describing an electron in an external electric field E
1
H =
2m
- eɛx
(a) Use the commutation relations between the operators x and p to obtain the equations of motion describing the
time-dependence of (x) and (p).
(b) Solve the equations of motion from (a) above and express the solutions in terms of initial values of x and p, i.e.
x(0) and p(0)t.
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