The expectation values are also reported for the 119 systems considered in the present study.

Thus the expectation value of energy is also time independent.

What would the expectation value of the mutual information be?

If this is not the case, then the expectation values are meaningless.

The expectation value which can be thought of as all directions being equally likely.

In these cases, the expectation value is determined only by the more general formula (6).

A precise definition of this expectation value is given below.

The evolution of the expectation value does not depend on this choice, however.

The score and expectation values are also direct from the database.

These are only the expectation values of and for the state .

What is the expectation value of h if f and g are not independent?

The expectation values are with respect to the bath degrees of freedom.

That is we always want the expectation value of the normal ordered product to be zero.

It says that the expectation value of the operator A remains constant in time.

These vacuum expectation values can take any value for which the potential function is a minimum.

The energy corrections due to the applied field are given by the expectation value of in the basis.

So its average values (expectation values) in those two cases are different.

The situation in quantum field theory is rather different: the expectation value of the energy density can be negative at any given point.

Similarly we can obtain the instantaneous change in the position expectation value.

These matches are usually reported with a measure of statistical significance such as an Expectation value.

It will provide students an opportunity to utilize probability (expectation values) in a real world situation.

Either or (the conjugation of the first) can be used to minimize the expectation value.

Which definition is most appropriate depends on the expectation values needed for a given calculation.

For non-ergodic systems there is no general reason why expectation values should have any relevance.

To properly median filter the data the expectation value of the signal should be the same.