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All the conserved physical processes can be expressed as proper \(\text{ Hamiltonian }\) systems, and their common mathematical basis is the symplectic space. Unlike the Euclidean space, which investigates metric properties such as length, the symplectic space studies the area or the work instead [28]. The eigenfunction system of an infinite-dimensional \(\text{ Hamiltonian }\) operator is symplectic orthogonal. Therefore, this section takes the symplectic structure as the main line, and briefly introduces the infinite-dimensional complex symplectic space and some other basic properties.

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Completeness of Eigenvector System of Infinite-Dimensional Hamiltonian Operators

  • 章节

  • 发表日期：

    2026年

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  • Alatancang Chen,
  • Deyu Wu,
  • Junjie Huang,
  • Guolin Hou

摘要

All the conserved physical processes can be expressed as proper \(\text{ Hamiltonian }\) systems, and their common mathematical basis is the symplectic space. Unlike the Euclidean space, which investigates metric properties such as length, the symplectic space studies the area or the work instead [28]. The eigenfunction system of an infinite-dimensional \(\text{ Hamiltonian }\) operator is symplectic orthogonal. Therefore, this section takes the symplectic structure as the main line, and briefly introduces the infinite-dimensional complex symplectic space and some other basic properties.