Biorthogonal Quantum Mechanics pdf


Biorthogonal Quantum Mechanics pdf

Biorthogonal Quantum Mechanics pdf

In standard quantum mechanics observable quantities are characterised by Hermitian operators. The eigenvalues of a Hermitian operator represent possible outcomes of the measurement of an observable represented by that operator. Once the measurement of, say, the energy is performed and the outcome recorded, the system is in a state of definite energy, that is, there cannot be a transition into another state with a different energy. Hermitian operators conveniently encode this feature in the form of the
orthogonality of their eigenstates.

The observed lack of transition into another state, however, can only be translated into the abstract ‘mathematical’ notion of the orthogonality of states in Hilbert space via the specification of the probability rules in quantum mechanics. When eigenstates of an observable are not orthogonal, however, there is an equally natural way of assigning probability rules so that the resulting quantum theory appears identical to the conventional theory

Get your DOC 1 : By Dorje C. Brody

Biorthogonal quantum mechanics of neutral bosons : Margaret Hawton · Vincent Debierre

Phase transitions and generalized biorthogonal polarization in non-Hermitian systems : Elisabet Edvardsson,Flore K. Kunst , Tsuneya Yoshida and Emil J. Bergholtz

Consistency of PT-symmetric quantum mechanics : Dorje C. Brody

Non-Hermitian Chiral Magnetic Effect in Equilibrium : Maxim N. Chernodub and Alberto Cortijo


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