Solved: The Hamiltonian of a two – level quantum system is 𝐻 = 1 2 ℏ πœ” ( [ 1 , 1 ] , [ 1 , – 1 ] )

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The Hamiltonian of a two-level quantum system is 𝐻=12β„πœ”([1,1],[1,-1]).Β A possible initial state in which the probability of the system being in that quantum state does not change with time, is
(a)Β (π‘π‘œπ‘ (πœ‹4)𝑠𝑖𝑛(πœ‹4))
(b)Β (π‘π‘œπ‘ (πœ‹8)𝑠𝑖𝑛(πœ‹8))
(c)Β (π‘π‘œπ‘ (πœ‹2)𝑠𝑖𝑛(πœ‹2))
(d)Β (π‘π‘œπ‘ (πœ‹6)𝑠𝑖𝑛(πœ‹6))

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