Answer to Question #207395 in Quantum Mechanics for Prugs

Question

Consider two eigenstates |𝑢1

⟩ and |𝑢2

⟩ of an observable satisfy the 

condition ⟨𝑢1

|𝑢2

⟩ = 4 and ⟨𝑢1

|𝑢1

⟩ = ⟨𝑢2

|𝑢2

⟩ = 1. Find a normalized 

linear combination of |𝑢1

⟩ and |𝑢2

⟩ ,i.e., (𝑎|𝑢1

⟩ +

𝑏|𝑢2

⟩, where a and b are real constant) which is orthogonal to (|𝑢1

⟩ −

|𝑢2

⟩).

Answer 1

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