SpaceKine Spectral Decomposition of Hamiltonian Operator without Imaginary Numbers

Spectral Decomposition of Hamiltonian Operator without Imaginary Numbers

April 2024

DOI: 10.13140/RG.2.2.30992.83200

Zenghao Yao

https://www.researchgate.net/publication/379496038_Spectral_Decomposition_of_Hamiltonian_Operator_without_Imaginary_Numbers

Hamiltonian operator does not contain imaginary numbers in its spectral decomposition:

Pure point: Trigonometric functions with k greater than 0

Absolutely continuous: Exponential functions with k greater than 0

Singular continuous: Undamped multi-degree-of-freedom free simple harmonic vibrations with k less than 0

Imaginary numbers arise from the symmetry of left-handedness and right-handedness.

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