Physical interpretation of non-normalizable harmonic oscillator states and relaxation to pilot-wave equilibrium.

ABSTRACT: Non-normalizable states are difficult to interpret in the orthodox quantum formalism but often occur as solutions to physical constraints in quantum gravity. We argue that pilot-wave theory gives a straightforward physical interpretation of non-normalizable quantum states, as the theory requires only a normalized density of configurations to generate statistical predictions. In order to better understand such states, we conduct the first study of non-normalizable solutions of the harmonic oscillator from a pilot-wave perspective. We show that, contrary to intuitions from orthodox quantum mechanics, the non-normalizable eigenstates and their superpositions are bound states in the sense that the velocity field [Formula: see text] at large [Formula: see text]. We argue that defining a physica

SUBMITTER: Sen I 

PROVIDER: S-EPMC10787783 | biostudies-literature | 2024 Jan

REPOSITORIES: biostudies-literature