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Biorthogonal systems on unit interval and zeta dilation operators
Dorje C Brody
An elementary 'quantum-mechanical' derivation of the conditions for a system of functions to form a Reisz basis of a Hilbert space on a finite interval is presented.
Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian
Carl M. Bender, Dorje C. Brody
The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed…
A Riemannian approach to Randers geodesics
Dorje C. Brody, Gary W. Gibbons, David M. Meier
In certain circumstances tools of Riemannian geometry are sufficient to address questions arising in the more general Finslerian context. We show that one such instance presents it…
Complex extension of Wigner's theorem
Dorje C. Brody
Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that w…
Coquaternionic quantum dynamics for two-level systems
Dorje C. Brody, Eva-Maria Graefe
The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristic…
On complexified mechanics and coquaternions
Dorje C Brody, Eva-Maria Graefe
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been…