Chapter 20. The wave function and its interpretation

Alyssa Ney

Abstract This chapter considers and responds to criticism that wave function realism is only plausible as an approach to the interpretation of nonrelativistic quantum mechanics and not relativistic quantum theories and quantum field theories. This critique gains traction as wave function realism has until now been formulated and defended solely within the context of idealized, nonrelativistic quantum mechanics. The chapter considers five such arguments and responds to each. An important lesson is that wave function realists should only adopt the wave-function-in-configuration-space picture as part of an interpretation of an idealized nonrelativistic quantum mechanics. More generally, the space the wave function inhabits will vary as the quantum theory the wave function realist is developing an interpretation of varies. The chapter develops a sketch of what wave function realism looks like in one relativistic context. It then discusses the issue of the interpretation of quantum theories in the limit of physical theorizing.

R. Shankar

Масуд Чайчиан, Rolf Hagedorn

This chapter discusses everything in terms of wave functions and describes the choice between active and passive rotations. It defines the representations of the rotation group by means of the abstract state vectors and by means of wave functions. That implies that the rotations are active rotations. The chapter finds that for a sequence of rotations the three-dimensional matrices have the property. It considers the change of the wave function in active and passive rotations respectively. In the active interpretation the physical system — characterized in space by the wave function — is bodily rotated. In the passive interpretation the frame of reference is rotated, whereas P and the local physical state at P remain unchanged. The chapter describes that there is a description which uses the new coordinates but describes the old situation.

Mark S. Swanson

Chapter 3 presents the Copenhagen interpretation of the wave function in terms of probability and experimental preparation. Fourier analysis is applied to determine the wave function of a particle in a box.