Expectation Value of Operator A: c or Complex Conjugate?

In summary, when taking a complex constant c outside of the bracket in the expectation value <psi | cA | psi>, it remains as c and does not need to be complex-conjugated. This is due to the linearity of quantum mechanics operations. Only in cases of time-reversal, where anti-linear operators are introduced, do constants need to be complex-conjugated.
  • #1
dyn
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If I have the following expectation value for a general operator A < psi | cA | psi > where c is a complex constant and I want to take c outside the bracket does it go as c or its complex conjugate ?
 
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  • #2
dyn said:
If I have the following expectation value for a general operator A < psi | cA | psi > where c is a complex constant and I want to take c outside the bracket does it go as c or its complex conjugate ?

You take c outside, and do not complex-conjugate it. You can always view the bra <psi| as a linear operator on kets, and since A|psi> is a ket bringing c outside is fine. Almost all operations in QM are linear, and complex constant can be taken outside of linear operators. When you deal with time-reversal, you introduce anti-linear operators where you do have to complex-conjugate constants to bring them outside, but this is not the case here.
 

Related to Expectation Value of Operator A: c or Complex Conjugate?

1. What is the expectation value of operator A?

The expectation value of operator A is a mathematical concept used in quantum mechanics to describe the average value of a physical quantity in a given state.

2. What is the significance of the expectation value?

The expectation value of operator A is significant because it allows us to predict the most likely outcome of a measurement for a particular physical quantity in a given state.

3. What is the difference between c and complex conjugate in the expectation value of operator A?

In the expectation value of operator A, c refers to the complex number that represents the amplitude of a particular state, while complex conjugate refers to the complex number obtained by changing the sign of the imaginary part of c.

4. How is the expectation value of operator A calculated?

The expectation value of operator A is calculated by taking the inner product of the operator with the state vector, and then taking the complex conjugate of the result.

5. How does the expectation value of operator A relate to the uncertainty principle?

The expectation value of operator A is related to the uncertainty principle as it represents the average value of a physical quantity, which can never be determined with complete certainty due to the inherent uncertainty in quantum mechanics.

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