Virial theorem and generalized momentum in quaternic quantum mechanics

Abstract

After a review on recent results on quaternic quantum mechanics ($\mathbb{H}$QM), we present further consistency tests that reinforce its compatibility with the usual complex quantum mechanics ($\mathbb{C}$QM). The novel results comprises the Virial theorem, the quantum quaternic Lorentz force, the existence of a quaternic magnetic monopole and the redefinition of the expectation value.

Accept by Eur. Phys. J. Plus

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• Simulating quantum systems using real Hilbert spaces
• Quaternionic Wave Packets
• Quaternionic perturbation theory

Cited by in corpus (16)

• Quaternionic Klein-Gordon equation
• Quaternionic quantum harmonic oscillator
• Quaternionic elastic scattering
• Quaternionic Dirac free particle
• Quaternionic scalar field in the real Hilbert space
• Quaternionic fermionic field
• Spin and angular momentum in quaternionic quantum mechanics
• Expectation value dynamics within real Hilbert space quantum mechanics
• Self-interacting quantum particles
• A possibility of Klein Paradox in quaternionic (3+1) frame
• Klein-Gordon equation within the real Hilbert space formalism
• Quantum self-interaction within an infinitely deep cavity
• Generalized imaginary units in quantum mechanics
• Deformed angular momentum algebra within the real Hilbert space
• The quantum harmonic oscillator and the real Hilbert space
• On the existence of quaternion-handedness for the spinor solutions of the Dirac and Majorana neutrinos