Consider a simple harmonic oscillator in one dimension. Do the following algebraically, that is, without using wavefunctions. a) Construct a linear combination of |0) and |1) such that the expected position (x) is as large as possible b) Suppose the oscillator is in the state you found in part (a) at time t - vector for t> 0 in the Schrödinger picture? Evaluate the expectation value (x) at time t using (i) the Schrödinger picture and (ii) the Heisenberg picture. 0. What is the state c) Evaluate the uncertainty in position, ((Ax)) as a function of time using either picture.
Consider a simple harmonic oscillator in one dimension. Do the following algebraically, that is, without using wavefunctions. a) Construct a linear combination of |0) and |1) such that the expected position (x) is as large as possible b) Suppose the oscillator is in the state you found in part (a) at time t - vector for t> 0 in the Schrödinger picture? Evaluate the expectation value (x) at time t using (i) the Schrödinger picture and (ii) the Heisenberg picture. 0. What is the state c) Evaluate the uncertainty in position, ((Ax)) as a function of time using either picture.
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Transcribed Image Text:Consider a simple harmonic oscillator in one dimension. Do the following algebraically, that is,
without using wavefunctions.
a) Construct a linear combination of |0) and |1) such that the expected position (x) is as large as
possible
b) Suppose the oscillator is in the state you found in part (a) at time t -
vector for t> 0 in the Schrödinger picture? Evaluate the expectation value (x) at time t using (i)
the Schrödinger picture and (ii) the Heisenberg picture.
0. What is the state
c) Evaluate the uncertainty in position, ((Ax)) as a function of time using either picture.
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