Quantum Theory of Coupled Systems Having Application to Masers

Non-relativistic quantum mechanics is treated using Feynman's space-time approach and Wigner's probablity density of position and momentum. The mechanics of a system is described by the probability of each path of the coordinates in space-time. The influence of one system on another is described by the probability of a force function. It is shown that linear systems follow only classical paths. The quantum theory merely puts uncertainty into their initial conditions, just like thermal noise. The formalism apparently does not simplify intrinsically non-linear problems. However, linear systems are sometimes coupled to non-linear quantum systems which operate only on a linear portion of their charactersitcs (like a vacuum tube in a class A amplifier). Then the reaction on the linear systems can be reduced to an equivalent impedence and noise power spectrum, so that the linear problem can be solved by classical methods. Solid state and beam type masers are treated as examples. Masers employ excited non-linear systems to acheive linear amplification of the electromagnetic signal. The modes of the waveguides and cavities are the linear systems. To them the amplifying systems appear as nagative resistance, reactance, and noise