2.12 A one-dimensional simple harmonic oscillator with natural frequency w is in initial state 1 |a) = where is a real number. =|0) + √2 eið √2/1) :|1) a. Find the time-dependent wave function (x'a; t) and evaluate the (time-dependent) expectation values (x) and (p) in the state |a; t), i.e. in the Schrödinger picture. b. Now calculate (x) and (p) in the Heisenberg picture and compare the results.
2.12 A one-dimensional simple harmonic oscillator with natural frequency w is in initial state 1 |a) = where is a real number. =|0) + √2 eið √2/1) :|1) a. Find the time-dependent wave function (x'a; t) and evaluate the (time-dependent) expectation values (x) and (p) in the state |a; t), i.e. in the Schrödinger picture. b. Now calculate (x) and (p) in the Heisenberg picture and compare the results.
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Transcribed Image Text:2.12 A one-dimensional simple harmonic oscillator with natural frequency w is in initial
state
1
|a)
=
where is a real number.
=|0) +
√2
eið
√2/1)
:|1)
a. Find the time-dependent wave function (x'a; t) and evaluate the (time-dependent)
expectation values (x) and (p) in the state |a; t), i.e. in the Schrödinger picture.
b. Now calculate (x) and (p) in the Heisenberg picture and compare the results.
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