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Acquiring the Symplectic Operator Based on Pure Mathematical Derivation then Verifying It in the Intrinsic Problem of Nanodevices

The Department of Information and Communication Engineering, Tongji University, Shanghai 200092, China
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Symmetry 2019, 11(11), 1383; https://doi.org/10.3390/sym11111383
Received: 8 October 2019 / Revised: 4 November 2019 / Accepted: 4 November 2019 / Published: 7 November 2019
The symplectic algorithm can maintain the symplectic structure and intrinsic properties of the system, its cumulative error is small and suitable for multi-step calculation. At present, the widely accepted symplectic operators are obtained by solving the Hamilton equation based on artificial definitions and assumptions in advance. There are inevitable dispersion errors. We solve the equation by pure mathematical derivation without any artificial limitations and assumptions. The way to accurately obtain high-precision symplectic operators greatly reduces the dispersion error from the beginning. The numerical solution of the one-dimensional Schrödinger equation for describing the intrinsic problem of nanodevices is used as an application environment to compare the total energy distribution of the particle wave function in the box, thus verifying the properties of the Symplectic Operator based on Pure Mathematical Derivation by comparing with Finite-Difference Time-Domain (FDTD) and the widely accepted symplectic operator.
Keywords: pure mathematical derivation; symphony; dispersion analysis; Schrödinger equation; Hamiltonian system pure mathematical derivation; symphony; dispersion analysis; Schrödinger equation; Hamiltonian system
MDPI and ACS Style

Nie, H.; Gui, R.; Chen, T. Acquiring the Symplectic Operator Based on Pure Mathematical Derivation then Verifying It in the Intrinsic Problem of Nanodevices. Symmetry 2019, 11, 1383.

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