An expectation value is a statistical concept used in quantum mechanics to predict the average outcome of a measurement on a system. It is calculated by multiplying the probability of each possible measurement outcome by the value of that outcome and then summing all of these products together.
An expectation value is a theoretical concept that represents the average outcome of a measurement, whereas a measurement is an actual observation of a physical quantity. The expectation value is a prediction based on the probability of different outcomes, while a measurement is an actual result obtained by performing an experiment.
Expectation values are considered "real" because they provide a way to calculate the average value of a physical quantity that is consistent with the probabilistic nature of quantum mechanics. They have been verified through numerous experiments and have been found to accurately predict the outcomes of measurements.
Yes, expectation values can be negative. In quantum mechanics, physical quantities can have both positive and negative values, and the expectation value represents the average of all possible outcomes. Therefore, it is possible for an expectation value to be negative if some of the possible outcomes have negative values.
Operators are mathematical representations of physical quantities in quantum mechanics. They are used to calculate the expectation value of a quantity by acting on the state function of the system. The expectation value is then obtained by taking the inner product of the operator with the state function. In this way, operators play a crucial role in determining the expectation value of a physical quantity.