By Ralph Decker Bennett
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Extra resources for An Attempt to Test the Quantum Theory of X-Ray Scattering
The law of conservation of angular momentum (of all its components) with respect to the origin of a co-ordinate system is valid in a closed system. We proved this result, since under a rotation the properties of a closed system do not change. e. in an open system, if the field possesses a symmetry axis. Then, under a rotation about this axis the mechanical properties of the system won't change. Therefore, the projection of an angular momentum on this axis, defined with respect to any axis point, remains constant.
By 2s quantities. During the motion of the system they are changed. But for the different systems some of these quantities and/or functions of them remain constants, which are determined by the initial conditions. They are called constants of the motion. Some constants of the motions can be found from the form of the Lagrangian function. 14) it is obvious that d ∂L = 0. 1) Consequently the generalized momentum Pi is a constant of the motion Pi = ∂L = const. 2) Such co-ordinates, on which the Lagrangian function does not depend, are called cyclic.
This condition is also valid for a system in a constant (with respect to time) external potential field. Hence the conservation law is valid also for such a system. The acting forces in such systems are conservative. Because of the importance of the conservative systems in chemistry we shall consider with more detail the rate of change of the energy and the character of the acting forces in such systems. We shall underline once more that this is a system in a constant field, depending only on the co-ordinates.
An Attempt to Test the Quantum Theory of X-Ray Scattering by Ralph Decker Bennett