Final answer:
The conjugate of the expectation value of an operator in quantum mechanics is the expectation value of the conjugate of that operator.
Step-by-step explanation:
The conjugate of the expectation value of an operator in quantum mechanics is the expectation value of the conjugate of the operator. This is because the expectation value involves an integral of the wave function and its complex conjugate, so conjugating the entire expression essentially means conjugating the operator within that integral. The wave function, Ψ, is generally complex, and when calculating probabilities or expectation values, the product of Ψ and its complex conjugate, Ψ*, is used, ensuring resulting values are real numbers retrievable by experimental measurements. When we integrate with respect to the conjugate of an operator, we are therefore finding the expectation value of the conjugate of that operator.
The correct answer to the question is: 1) The expectation value of the conjugate of an operator.