Expectation Value of Operator A: c or Complex Conjugate?

Click For Summary
SUMMARY

The expectation value of a general operator A, represented as , allows the complex constant c to be taken outside the bracket without complex conjugation. This is due to the linear nature of quantum mechanics operations, where constants can be factored out of linear operators. In scenarios involving anti-linear operators, such as time-reversal, complex conjugation is necessary; however, this does not apply in the current context of expectation values.

PREREQUISITES
  • Understanding of quantum mechanics linear operators
  • Familiarity with expectation values in quantum mechanics
  • Knowledge of bra-ket notation
  • Concept of anti-linear operators in quantum mechanics
NEXT STEPS
  • Study the properties of linear operators in quantum mechanics
  • Learn about anti-linear operators and their implications in quantum mechanics
  • Explore the concept of time-reversal symmetry in quantum systems
  • Review examples of expectation values in various quantum mechanical contexts
USEFUL FOR

Quantum mechanics students, physicists, and researchers interested in the mathematical foundations of quantum theory and the manipulation of operators.

dyn
Messages
774
Reaction score
63
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 ?
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 8 ·
Replies
8
Views
1K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K