ABSTRACT
We assume that the four matrices α1, α2, α3, α4 are Hermitian and therefore the operator H is self-adjoint.
The so-called equation of motion for an operator F is
dF
dt =
∂F
∂t +
2πi h
This equation expresses the following mathematical fact.2 If one constructs a matrix ||Fmn|| using a complete system of solutions of equation(2), the time derivatives of the matrix elements
Fmn = ∫
ψmFψndxdydz (5)
are equal to the corresponding matrix elements of the right-hand side of (4), i.e.,
dFmn dt
= { ∂F
∂t +
2πi h
(HF − FH) }
. (6)
Equation (4) also has the following physical meaning. If F is an operator corresponding to a classical quantity, equation (4) yields the operator corresponding to its time derivative.
