A particular two-level quantum system has two eigenstates given by I8) := (9) le) := (¿) where |g) is the ground state and le) is the excited state. The Hamiltonian operator is given by A - (::) -A 0 a. Write down the density matrix and calculate for the partition function. b. Calculate for the mean energy of the system. c. Calculate for the expectation value of the operator o- (:) Ô = 0-1
A particular two-level quantum system has two eigenstates given by I8) := (9) le) := (¿) where |g) is the ground state and le) is the excited state. The Hamiltonian operator is given by A - (::) -A 0 a. Write down the density matrix and calculate for the partition function. b. Calculate for the mean energy of the system. c. Calculate for the expectation value of the operator o- (:) Ô = 0-1
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Transcribed Image Text:A particular two-level quantum system has two eigenstates given
by
Ig) := (9)
le) := (¿)
where |g) is the ground state and le) is the excited state. The
Hamiltonian operator is given by
Îû = ()
O A
a. Write down the density matrix and calculate for the partition
function.
b. Calculate for the mean energy of the system.
c. Calculate for the expectation value of the operator
1 0
0-1
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