# Quantum inner-product metrics via the recurrent solution of the Dieudonné equation

@article{Znojil2012QuantumIM, title={Quantum inner-product metrics via the recurrent solution of the Dieudonn{\'e} equation}, author={M. Znojil}, journal={Journal of Physics A}, year={2012}, volume={45}, pages={085302} }

A given Hamiltonian matrix H with a real spectrum is assumed tridiagonal and non-Hermitian, H ? H?. Its possible Hermitizations via an amended, ad hoc inner-product metric ? = ?? > 0 are studied. Under certain reasonable assumptions, all of these metrics ? = ?(H) are shown to be obtainable as recurrent solutions of the hidden Hermiticity constraint H??? = ??H called the Dieudonn? equation. In this framework, even the two-parametric Jacobi-polynomial real and asymmetric N-site lattice H(N… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 17 REFERENCES

An exactly solvable quantum-lattice model with a tunable degree of nonlocality

- Physics, Mathematics
- 2011

12

Symbolic-Manipulation Constructions of Hilbert-Space Metrics in Quantum Mechanics

- Computer Science, Physics
- 2011

2