Mathematical Methods in Classical and Quantum Mechanics
An adjoint operator is a linear operator associated with a given linear operator that reflects the relationship between two inner product spaces. It is defined such that for any two vectors in the space, the inner product of the operator's output and another vector corresponds to the inner product of the first vector and the adjoint operator applied to the second. This concept plays a crucial role in understanding the properties of operators, including self-adjointness and unitary operators, and forms a foundation for more complex mathematical structures in quantum mechanics.
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