Invariant Eigen-Structure in Complex-Valued Quantum Mechanics
- URL: http://arxiv.org/abs/2103.10981v1
- Date: Fri, 19 Mar 2021 18:37:39 GMT
- Title: Invariant Eigen-Structure in Complex-Valued Quantum Mechanics
- Authors: C. D. Yang, S. Y. Han
- Abstract summary: The complex-valued quantum mechanics considers quantum motion on the complex plane instead of on the real axis.
It is revealed that the conventional real-valued quantum mechanics is a special case of the complex-valued quantum mechanics.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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