Consider an operator  that contains the time as a parameter. We are interested in how the average value of the property A changes with time, and we have

The definite integral on the right side of this equation is a function of the parameter t, and it is generally a valid mathematical operation to calculate its derivative with respect to t by differentiating the integrand with respect to t:

Transcribed Image Text:

dt dt ja|v.AV ) dr Ja ΑΨ dr + fydat Vir + j Ψ.Aaat dr öt at/h