Invariant eigen-structure in complex-valued quantum mechanics

Ciann Dong Yang, Shiang Yi Han

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


The complex-valued quantum mechanics considers quantum motions on a complex plane instead of on a real axis, and presents variations of a particle's complex position, momentum and energy along a complex trajectory. On the basis of quantum Hamilton-Jacobi formalism in the complex space, we point out that having complex-valued motions is a universal property for quantum systems because every quantum system is actually accompanied with an intrinsic complex Hamiltonian derived from the Schrodinger equation. It is revealed that the conventional real-valued quantum mechanics is a special case of the complex-valued quantum mechanics in which eigen-structures of real and complex quantum systems, such as their eigenvalues, eigenfunctions and eigen-trajectories, are invariant under linear complex mapping. In other words, there is indeed no distinction between Hermitian, PT-symmetric, and non PT-symmetric systems when viewed from a complex domain. Their eigen-structures can be made coincident through linear transformations of complex coordinates.

Original languageEnglish
Pages (from-to)407-423
Number of pages17
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
Issue number4
Publication statusPublished - 2009

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Computational Mechanics
  • Modelling and Simulation
  • Engineering (miscellaneous)
  • Mechanics of Materials
  • General Physics and Astronomy
  • Applied Mathematics


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