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Soviet physics. Doklady

Quantities in the Theory of Angular Momentum with Negative Parameters Representing the Quantum Numbers of the Angular Momentum

A. Bandzaitis, A.V. Karosene, A.Yu. Savukinas, A. P. Yutsis

Published Aug 1, 1964• 1 citation
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In the first part of this chapter we shall show how it is possible to represent dynamical variables by matrices instead of differential operators without affecting the predicted results of physically significant quantities. We shall see that, although this representation is often more complicated and cumbersome than the methods used earlier, it has a particularly simple form when applied to problems involving angular momentum, and has the great advantage that it can be used in the case of spin where no differential operator representation exists. We shall use such spin matrices to analyze experiments designed to measure the components of spin in various directions and find that these provide an important and illustrative example of the quantum theory of measurement.
A particle moving along a straight-line has a linear momentum mv. A revolving particle has angular momentum due to its mass and angular velocity. Let us imagine the electron as a small ball, revolving about some axis. It possesses angular momentum. Precisely, the angular momentum vector is a vector pointing along the axis of rotation with magnitude proportional to the speed of rotation. In classical mechanics the symmetry of a physical system leads to conservation laws. If the space is isotropic, it possesses rotational symmetry. The number of elements in a group is called its order. A group with finite number of elements is called a finite group whereas an infinite group contains infinite number of elements. An infinite group may further be either discrete or continuous. In fact, it is impossible to tell whether an electron is spinning. The word spin is a convenient way of representing the intrinsic angular momentum of a particle.