Consider a one-dimensional harmonic oscillator at the initial (i.e., ( t=0) ) state
[
|psi(0)
angle=frac{|1
angle+|2
angle}{sqrt{2}}
]
where ( |1
angle ) and ( |2
angle ) are first two excited states, respectively.
(a) In the Schrodinger representation, what is the state vector ( |psi(t)
angle ) for ( t geq 0 ) ?
(b) Evaluate ( langlehat{X}
angle,langlehat{P}
angle,leftlanglehat{X}^{2}
ight
angle ) and ( leftlanglehat{P}^{2}
ight
angle ) as functions of time when ( t=0 ) in the Schrodinger representation.
(c) Repeat component (b) for the Heisenberg representation.
( [10] )
