Probabilistic Interpretation of Resonant States

Understand

We provide probabilistic interpretation of resonant states.

• This we do by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of time, and therefore leads to probability conservation.
• This is in contrast with the conventional employment of a bi-orthogonal basis that precludes probabilistic interpretation, since wave functions of resonant states diverge exponentially in space.
• On the other hand, resonant states decay exponentially in time, because momentum leaks out of the central scattering area.