PHY4221Fall05_Quiz4

PHY4221Fall05_Quiz4 - and | 2 i and | 1 i are the...

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PHY4221 Quantum Mechanics I (Fall 2005) Quiz 4 Consider a two-level system coupled to a simple harmonic oscillator, whose Hamil- tonian operator is given by ˆ H = ¯ 0 ± ˆ a ˆ a + 1 2 + Ω ( | 2 ih 2 | - | 1 ih 1 | ) + λ ˆ a | 1 ih 2 | + | 2 ih 1 | ˆ a · where ˆ a and ˆ a are the lowering and raising operators of the simple harmonic oscillator,
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Unformatted text preview: and | 2 i and | 1 i are the eigenstates of the two-level system. Find the eigenenergies and eigenvectors of the ground state and first excited state of the system....
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