Question

A quantum mechanical system starts out in the state $left|psi(0) ight angle = C(3left|a_1 ight angle + 4left|a_2 ight angle)$, where $left|a_i ight angle$ are the normalized eigenstates of the operator A corresponding to the eigenvalues $a_i$. In this $left|a_i ight angle$ basis, the Hamiltonian of this system is represented by the matrix $H = E_0 egin{pmatrix} 2 & 1\ 1 & 2 end{pmatrix}$. a) If you measure the energy of this system, what values are possible, and what are the probabilities of measuring those values? b) Calculate the expectation value $langle A angle$ of the observable A as a function of time.

          A quantum mechanical system starts out in the state
$left|psi(0)
ight
angle = C(3left|a_1
ight
angle + 4left|a_2
ight
angle)$, 
where $left|a_i
ight
angle$ are the normalized eigenstates of the operator A corresponding to the eigenvalues $a_i$.
In this $left|a_i
ight
angle$ basis, the Hamiltonian of this system is represented by the matrix
$H = E_0 egin{pmatrix} 2 & 1\ 1 & 2 end{pmatrix}$.
a) If you measure the energy of this system, what values are possible, and what are the
probabilities of measuring those values?
b) Calculate the expectation value $langle A 
angle$ of the observable A as a function of time.

A quantum mechanical system starts out in the state
left|psi(0)
ight
angle = C(3left|a1
ight
angle + 4left|a2
ight
angle),
where left|ai
ight
angle are the normalized eigenstates of the operator A corresponding to the eigenvalues ai.
In this left|ai
ight
angle basis, the Hamiltonian of this system is represented by the matrix
H = E0 eginpmatrix 2 1 1 2 endpmatrix.
a) If you measure the energy of this system, what values are possible, and what are the
probabilities of measuring those values?
b) Calculate the expectation value langle A
angle of the observable A as a function of time.

Added by Gloria R.

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