Quanta and Their States

“Quantum states” are an extension, to quantized fields, of the states or configurations of classical fields. A quantum is a highly unified, spatially extended, bundle of field energy that can be configured or prepared in various ways just as a classical field’s energy can be configured in various ways (Figs.  3.3 – 3.7 ). Like states of the classical EM field, two or more quantum states can be superposed (Chap. 8 ). The quantum state \(\Psi \left( {r,t} \right)\) of, say, an electron represents something real: the spatial distribution of the electron’s field energy. The Born rule gives experimental meaning to quantum states: \(\left| {\Psi \left( {r,t} \right)} \right|^{2}\) is the probability density that a detection, if carried out at time t, will occur at point r. “Detection” refers to an interaction between a quantum and a detector that is then amplified irreversibly. Confined quanta must obey certain boundary conditions which often limit their possible states to discrete values of the quantum’s energy or other physical quantities. Changes in these values then entail “quantum jumps” between allowed values. We analyze the stationary states of Schrodinger’s equation—the states of a single nonrelativistic quantum in which \(\left| {\Psi \left( {r,t} \right)} \right|^{2}\) is time-independent. As an example of quantum states, we study the stationary states of the hydrogen atom. As expected from the unity of each quantum of energy, transitions between these states occur instantaneously. This was verified experimentally in 1986. We also study the “Rydberg” states of hydrogen-like atoms as examples of how quantum predictions become classical, and the field spreading of free quanta in space.