Odd dimensional translation between complex and quaternionic quantum mechanics

Jonathan Gantner

Stefano De Leo, Waldyr A. Rodrigues

C. G. Nash, Gayatri Joshi

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.

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.

Lawrence Paul Horwitz, Lawrence C. Biedenharn, Daniel Sepunaru