Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Translations between quaternion and complex quantum mechanics

De Leo, S, Rotelli, P

Published Dec 14, 1993• 18 citations
OpenAlex

Abstract

While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a {\\em partial} set of {\\em translations} may be made. We define these translations and use the rules to obtain rapid quaternion counterparts (some of which are new) of standard quantum mechanical results.

Related papers

Translations between Quaternion and Complex Quantum Mechanics

S. De Leo, P. Rotelli

While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a partial set of translations may be made. We define these translations and use the rules to obtain rapid quaternion counterparts (some of which are new) of standard quantum mechanical results.

arXiv:hep-th/9401009•Progress of Theoretical Physics•Nov 1, 1994•18 citations

Translations between Quaternion and Complex Quantum Mechanics

Stefano De Leo, PIETRO P. ROTELLI

While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a partial set of translations may be made. We define these translations and use the rules to obtain rapid quaternion counterparts (some of which are new) of standard quantum mechanical results.

Progress of Theoretical Physics•Nov 1, 1994•10 citations

Odd Dimensional Translation between Complex and Quaternionic Quantum Mechanics

Stefano De Leo, PIETRO P. ROTELLI

We complete the rules of translation between standard complex quantum mechanics (CQM) and quaternionic quantum mechanics (QQM) with complex geometry. In particular we describe the way in which (2n+1)-dimensional complex matrices are reduced to overlapping (n+1)-dimensional quaternionic matrices with generalized quaternionic elements. This step resolves an outstanding difficulty with reduction of purely complex matrix groups within quaternionic QM and avoids anomalous eigenstates. As a result we present a more complete translation from CQM to QQM and vice versa.

arXiv:hep-th/9605021•Progress of Theoretical Physics•Jul 1, 1996•14 citations

Further General Results in Quaternionic Quantum Mechanics

Stephen L. Adler

Abstract We next discuss certain general results in quaternionic quantum mechanics, which can be formulated independently of the detailed structure of the Hamiltonian H Our emphasis in this chapter will be on topics connected with symmetry generators. We introduce quaternion anti-self-adjoint space translation generators and use them to construct the momentum representation. Corresponding to these generators, we introduce several possible definitions for the self adjoint momentum operators and show that none of them possesses all the properties of the momentum in complex quantum mechanics. A closely analogous discussion is given for the rotation generators and angular momentum.

•Apr 27, 1995•0 citations

WKB approximation for quaternionic quantum mechanics with purely imaginary potentials

Bhashkar Singh, A. S. Rawat, Seema Rawat

Solving the Schrödinger equation in quaternionic quantum mechanics (QQM) has been a nut to crack. In complex quantum mechanics (CQM), approximation methods have been used to find the solutions of the Schrödinger equation when exact solutions are difficult to obtain. This study challenges the earlier Eikonal (or WKB) approximation formalism [S. L. Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, New York, 1995)] developed for an imaginary quaternion potential. In this paper, the correct form of coupled equations, obeying the noncommutative structure and approximated solution for quaternionic time-independent Schrödinger equation (QTISE), has been obtained.

International Journal of Modern Physics A•Jan 24, 2026•1 citation

Quaternionic elastic scattering

Sergio Giardino

Abstract We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ( QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for the case of a hard sphere scattering potential. The strong agreement between these new quaternionic results and the corresponding results in complex quantum mechanics reinforce the validity of the QM generalization of ordinary complex quantum mechanics ( QM).

arXiv:2011.05743•Europhysics Letters (EPL)•Dec 1, 2020•15 citations
While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a {\em partial} set of {\em translations} may be made. We define these translations and use the rules to obtain rapid quaternion counterparts (some of which are new) of standard quantum mechanical results.
We complete the rules of translation between standard complex quantum mechanics (CQM) and quaternionic quantum mechanics (QQM) with complex geometry. In particular we describe the way in which (2n+1)-dimensional complex matrices are reduced to overlapping (n+1)-dimensional quaternionic matrices with generalized quaternionic elements. This step resolves an outstanding difficulty with reduction of purely complex matrix groups within quaternionic QM and avoids anomalous eigenstates. As a result we present a more complete translation from CQM to QQM and vice versa.
Abstract We next discuss certain general results in quaternionic quantum mechanics, which can be formulated independently of the detailed structure of the Hamiltonian H Our emphasis in this chapter will be on topics connected with symmetry generators. We introduce quaternion anti-self-adjoint space translation generators and use them to construct the momentum representation. Corresponding to these generators, we introduce several possible definitions for the self adjoint momentum operators and show that none of them possesses all the properties of the momentum in complex quantum mechanics. A closely analogous discussion is given for the rotation generators and angular momentum.
Solving the Schrödinger equation in quaternionic quantum mechanics (QQM) has been a nut to crack. In complex quantum mechanics (CQM), approximation methods have been used to find the solutions of the Schrödinger equation when exact solutions are difficult to obtain. This study challenges the earlier Eikonal (or WKB) approximation formalism [S. L. Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, New York, 1995)] developed for an imaginary quaternion potential. In this paper, the correct form of coupled equations, obeying the noncommutative structure and approximated solution for quaternionic time-independent Schrödinger equation (QTISE), has been obtained.