vela said:Nope.
Oxvillian said:However, the combination
[tex]D = \frac{XP+PX}{2},[/tex]
which looks the same classically, is self adjoint. One can often construct valid observables by getting the operator ordering right.
The expectation value of a non-physical observable is a statistical measure of the average value that would be obtained from a large number of measurements of that observable in a given quantum state. It is a mathematical concept used in quantum mechanics to describe the expected behavior of a system.
The expectation value of a non-physical observable is calculated by taking the inner product of the state vector with the observable operator. This is then multiplied by the complex conjugate of the state vector and integrated over all possible values of the observable. The result is a single number that represents the average value of the observable in that state.
Yes, the expectation value of a non-physical observable can be negative. In quantum mechanics, the expectation value is a probability-weighted average, so it is possible for the average value to be negative if the probabilities for different outcomes are appropriately weighted.
The uncertainty principle states that it is impossible to know with certainty both the position and momentum of a particle at the same time. This principle also applies to other non-physical observables. Therefore, the expectation value of a non-physical observable may have a larger uncertainty due to the inherent uncertainty in the quantum system.
The expectation value of a non-physical observable is a fundamental concept in quantum mechanics and plays a crucial role in predicting the behavior of a system. It allows scientists to make probabilistic predictions about the outcomes of measurements and provides a way to compare different quantum states. It is also used in the formulation of important principles such as the conservation of energy and the uncertainty principle.