Systems that lack this property may have eigenmode crossings at exceptional points, which have been observed in microwave cavities. Bender and Boettcher proved that PT-symmetric systems have a “pseudo” form of this property, a fact used to create “cloaking” gratings and invisible sensors. Many open quantum systems with controlled dissipation can be described by an effective Hamiltonian that lacks this property, breaking probability conservation. Any two-level Hamiltonian with this property can be expressed as a superposition of the identity matrix and the (*) Pauli matrices. If an operator A has this property, then the exponential of i times A is unitary. Observables in quantum mechanics are assumed to have this property, which implies that eigenvalues are real and eigenvectors are orthogonal. For 10 points, name this property possessed by a matrix that equals its conjugate transpose. ■END■
ANSWER: Hermitian [or self-adjoint; prompt on conservative by asking “what property does that imply?”]
<Vincent Du, Physics>
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