Operator equations and Moyal products–metrics in quasi-Hermitian quantum mechanics
Copyright policy )Operator equations and Moyal products–metrics in quasi-Hermitian quantum mechanics
The Moyal product is used to cast the equation for the metric of a non-hermitian Hamiltonian in the form of a differential equation. For Hamiltonians of the form $p^2+V(ix)$ with $V$ polynomial this is an exact equation. Solving this equation in perturbation theory recovers known results. Explicit criteria for the hermiticity and positive definiteness of the metric are formulated on the functional level.
References added
- Stellenbosch University South Africa
Quantum Physics, Moyal product, non-Hermitian Hamiltonian, Perturbation theories for operators and differential equations in quantum theory, FOS: Physical sciences, Geometry and quantization, symplectic methods, Quantum Physics (quant-ph), 530, 510
Quantum Physics, Moyal product, non-Hermitian Hamiltonian, Perturbation theories for operators and differential equations in quantum theory, FOS: Physical sciences, Geometry and quantization, symplectic methods, Quantum Physics (quant-ph), 530, 510
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