Phase-amplitude separation of wave function as local gauge transformation Phase-amplitude separation of wave function as local gauge transformation

• Published in: Few-body systems Vol. 66; no. 3; p. 30
• Main Author: Rau, A. R. P.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 11.07.2025; Springer Nature B.V
• Subjects: Amplitudes; Atomic; Electrodynamics; Energy; Hadrons; Heavy Ions; Molecular; Nonlinear equations; Nuclear Physics; Optical and Plasma Physics; Particle and Nuclear Physics; Physics; Physics and Astronomy; Quantum mechanics; Quantum theory; Transformations (mathematics); Wave functions; Writing
• ISSN: 1432-5411; 0177-7963; 1432-5411
• DOI: 10.1007/s00601-025-02002-x

A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude and phase as real quantities that together carry the same information that is contained in the complex wave function. Two main avenues for doing so go way back in the history of the subject and have been used both for scattering and bound states. A connection is made here to gauge transformations of electrodynamics where the advent of quantum mechanics and later quantum field theory showed the central role that local gauge transformations play in physics.