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arXiv · 2103.10981

Invariant Eigen-Structure in Complex-Valued Quantum Mechanics

C. D. Yang·S. Y. Han
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Abstract

The complex-valued quantum mechanics considers quantum motion on the complex plane instead of on the real axis, and studies the variations of a particle 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 motion is a universal property of quantum systems, because every quantum system is actually accompanied with an intrinsic complex Hamiltonian originating from the equation. It is revealed that the conventional real-valued quantum mechanics is a special case of the complex-valued quantum mechanics in that the 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 systems, PT-symmetric systems, and non PT-symmetric systems when viewed from a complex domain. Their eigen-structures can be made coincident through linear transformation of complex coordinates.

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C. D. Yang, S. Y. Han. 2021-03-19. Invariant Eigen-Structure in Complex-Valued Quantum Mechanics. https://doi.org/10.1515/ijnsns.2009.10.4.407

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