Quantum Mechanical Equation of Motion

The equation of motion is a classical concept. Here we discuss a similar concept in Quantum Mechanics which describes the time evolution of the expectation values of Hermitian operators. Additional information before Equation (48). We see that E is a constant electric field, so its expectation value is also E. In the Hilbert space terminology the scaler product is usually called the "inner product" which is like the dot product between ordinary vectors.