Expectation value dynamics within real Hilbert space quantum mechanics
arXiv:2508.13332 · doi:10.1007/s10773-025-06111-5
Abstract
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The consistency of the formalism has been verified in terms of the continuity equation, the classical limit, and generalizations of the quantum Lorentz force, and the Virial theorem. Besides testing the consistency of the real Hilbert space approach, generalized position and angular momentum operators have been introduced, and inspire exciting directions for further research.
arXiv commentAccpet by Int. J. Theor. Phys
References in corpus (30)
- Quantum theory based on real numbers can be experimentally falsified
- Quantifying the Imaginarity of Quantum Mechanics
- Ruling out real-valued standard formalism of quantum theory
- Non-Hermitian quantum dynamics of a two-level system and models of dissipative environments
- 30 years in: Quo vadis generalized uncertainty principle?
- Hiding and masking quantum information in complex and real quantum mechanics
- Experimental refutation of real-valued quantum mechanics under strict locality conditions
- Unitary-invariant witnesses of quantum imaginarity
- Quaternionic quantum mechanics in real Hilbert space
- Non-anti-hermitian quaternionic quantum mechanics
- Resource Theory of Imaginarity: New Distributed Scenarios
- Virial theorem and generalized momentum in quaternic quantum mechanics
- New scattering features of quaternionic point interaction in non-Hermitian quantum mechanics
- Imaginarity of Gaussian states
- Quaternionic Aharonov-Bohm effect
- Positive maps and entanglement in real Hilbert spaces
- Quaternionic quantum particles
- Quaternionic quantum harmonic oscillator
- Quaternionic elastic scattering
- Quaternionic fermionic field
- Spin and angular momentum in quaternionic quantum mechanics
- Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
- Self-interacting quantum particles
- Exact solutions for time-dependent complex symmetric potential well
- Efficient discrimination between real and complex quantum theories
- Square-well potential in quaternic quantum mechanics
- Classical and quantum complex dynamics
- Multi-Path and Multi-Particle Tests of Complex vs. Hyper-Complex Quantum Theory
- Problems with Modified Commutators
- On the dual structure of the Schrödinger dynamics