Corpus ID: 237431008

A rigorous Hermitian proof about the G-dynamics and analogy with Berry-Keating's Hamiltonian

  title={A rigorous Hermitian proof about the G-dynamics and analogy with Berry-Keating's Hamiltonian},
  author={Jack Whongius},
Quantum covariant Hamiltonian system theory provides a coherent framework for modelling the complex dynamics of quantum systems. In this paper, we centrally deal with the Hermiticity of quantum operators that directly links to the physical observable, thusly, we give a rigorous proof to verify one-dimensional G-dynamics ŵ(cl) = ŵ(cl)† ∈ Her that is a Hermitian operator satisfying ( ŵ(cl)φ,φ ) = ( φ, ŵ(cl)φ ) for any two states φ and φ, and its eigenvalues are real. We also prove that curvature… Expand


Pseudo-Hermiticity versus PT symmetry : The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
We introduce the notion of pseudo-Hermiticityand show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in theExpand
Hamiltonian for the Zeros of the Riemann Zeta Function.
A heuristic analysis is presented for the construction of the metric operator to define an inner-product space, on which the Hamiltonian is Hermitian, and it is implied that the Riemann hypothesis holds true. Expand
Theory of linear operators in Hilbert space
linear operators in hilbert spaces | springerlink abstract. we recall some fundamental notions of the theory of linear operators in hilbert spaces which are required for a rigorous formulation of theExpand
E (s) /2 − √ −1 ŵ (cl) =Ĥ (g) −Ĥ (clm) ∈ N Her References
  • Ĥ (ri) =Ĥ (cl) −