Schrödinger Time Evolution Consider a Hamiltonian operator H and another operator Á corresponding to some observable. The matrix representations of Å and Ĥ in the energy basis are E (* :) - (3) where E > Ez and a is a real, positive number. (a) Find the measurement outcomes for Å and the associated eigenvectors. (Huge Hint: Â is proportional to another operator we know about. You are allowed to use this fact to greatly simplify this calculation.)
Schrödinger Time Evolution Consider a Hamiltonian operator H and another operator Á corresponding to some observable. The matrix representations of Å and Ĥ in the energy basis are E (* :) - (3) where E > Ez and a is a real, positive number. (a) Find the measurement outcomes for Å and the associated eigenvectors. (Huge Hint: Â is proportional to another operator we know about. You are allowed to use this fact to greatly simplify this calculation.)
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Transcribed Image Text:Schrödinger Time Evolution Consider a Hamiltonian operator Ĥ and another
operator Å corresponding to some observable. The matrix representations of Å and
Ĥ in the energy basis are
A- ( ) A-)
ÎĤ =
(3)
O E2
where E, > E, and a is a real, positive number.
(a) Find the measurement outcomes for Å and the associated eigenvectors. (Huge
Hint: Â is proportional to another operator we know about. You are allowed
to use this fact to greatly simplify this calculation.)
Transcribed Image Text:(b) Let the initial state (at t = 0) of the system be Ja1) where the outcome a, is
the largest eigenvalue of Å. Find the state as a function of time t.
(c) Calculate (A) as a function of time and show that the frequency associated
with (À) matches formula 3.21 in McIntyre.
(d) What is (H) as a function of time (for the same state as described in part b)?
Does this result make sense? Write 1-2 sentences about it.
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