- #1
adarlin
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If we have two linear operators A, and B, where A+ is the adjoint of A, how do we prove the property,
(AB)+=(B+)(A+)
(AB)+=(B+)(A+)
Quantum Mechanics Adjoint Operators
- Thread starter adarlin
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To prove the property (AB)+=(B+)(A+), one must start by invoking the definitions of adjoint operators and the inner product. The adjoint of an operator A, denoted A+, satisfies the relation ⟨Ax, y⟩ = ⟨x, A+y⟩ for all vectors x and y. By applying this definition to the product of two operators AB, the proof involves manipulating the inner products and using the linearity of the operators. The discussion emphasizes the importance of understanding the underlying definitions and properties of adjoint operators to establish the proof correctly. Mastery of these concepts is crucial for further exploration in quantum mechanics.
for d), I am a bit confused. I have two trains of thoughts here
any thoughts on which answer is correct, and why the other one is incorrect? Both seem like valid solutions to me. Or is the question ambiguous?
thanks
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