A particle of mass m in a one-dimensional harmonic oscillator is initially in a state given by 亚(0)) 1 (|1) – |2)) where |n) are the time-independent eigenstates of the harmonic oscillator with corresponding energy eigenvalues En = ħw(n + }). (a) If one were to measure the energy of the particle in such state, what values would one get and what would be their associated probabilities? (b) Evaluate the time-dependent expectation values (r(t)) and (r²(t)) and from your results evaluate Ar = V(z?(t)) – (x)²
A particle of mass m in a one-dimensional harmonic oscillator is initially in a state given by 亚(0)) 1 (|1) – |2)) where |n) are the time-independent eigenstates of the harmonic oscillator with corresponding energy eigenvalues En = ħw(n + }). (a) If one were to measure the energy of the particle in such state, what values would one get and what would be their associated probabilities? (b) Evaluate the time-dependent expectation values (r(t)) and (r²(t)) and from your results evaluate Ar = V(z?(t)) – (x)²
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Transcribed Image Text:A particle of mass m in a one-dimensional harmonic oscillator is initially in a state given by
1
(11) – |2))
V2
|F(0))
-
where |n) are the time-independent eigenstates of the harmonic oscillator with corresponding energy eigenvalues
En = ħw(n + ).
(a) If one were to measure the energy of the particle in such state, what values would one get and what would be
their associated probabilities?
(b) Evaluate the time-dependent expectation values (x(t)) and (x²(t)) and from your results evaluate Ax =
V(?(t})) – (x)²
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