TABLE OF CONTENTS If a subsystem is isolated by impermeable walls, it can exist in one of the quantum states defined by the solution of the Schrodinger equation. If q represents all the coordinates and t is the time, then the possible states are given by the wave function as
where E n is the energy of the nth quantum state, h is Planck's constant, and u n( q) is the space part of the wave function, which is a function of coordinates only. The system will be in one of these states.
Isolated subsystems are unrealistic, so let us consider a subsystem that can exchange energy with its surroundings. It cannot then stay in just one of the states given by (2.6.1). But, at any instant, we can expand the wave function of this subsystem in terms of those for the isolated subsystem as
This means that, at any instant, the probability of finding the subsystem in a state n is
so the subsystem is continually jumping among the state of the isolated subsystem with a probability given by (2.6.3). We will call p n( t) the instantaneous probability function.
Because of the uncertainty principle, the concept of an instantaneous probability function is not quite consistent with quantum mechanics. An energy change arising from the interaction of the subsystem with its surroundings can be precisely specified only if the time over which the energy change...
