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2. Consider two atoms, one described by the state vector |ψ1〉 = A1 |+〉−2A1 |−〉 and...

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Physics

2. Consider two atoms, one described by the state vector |ψ1〉 =A1 |+〉−2A1 |−〉 and the other by |ψ2〉 = A2 |+〉 − A2eiπ/4 |−〉 whereA1 and A2 are real constants.

(a) Calculate the constant A1.

(b) Calculate the constant A2.

(c) Calculate 〈ψ1|ψ2〉.
(d) Calculate 〈ψ2|ψ1〉.

(e) Derive a normalized vector |ψ3〉 that is orthogonal to|ψ1〉.

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