Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • adj. Equal to its own transpose conjugate.

Etymologies

from Wiktionary, Creative Commons Attribution/Share-Alike License

After the French mathematician Charles Hermite (1822–1901).

Examples

  • The observable is conserved if and only if the equations of motion are invariant under the transformations generated by the corresponding [Hermitian] operator

    Special Post: Noether’s First Theorem – Emmy Noether for Ada Lovelace Day

  • Hermitian operators in the Hilbert space associated with a system represent physical quantities, and their eigenvalues represent the possible results of measurements of those quantities.

    Quantum Mechanics

  • There are many cases in quantum mechanics where the Hamiltonian functions that represent the total energy of mechanical systems imitate those of classical mechanics, but with variables like those that stand for position and momentum replaced by Hermitian operators.

    Structural Realism

  • The only thing which is real are the eigenvalues of Hermitian operators.

    Quantum Hyperion

  • I tend to think of the expectation of a Hermitian operator as observable.

    Does Space Expand?

  • Strictly speaking an observable in QM is determined by a Hermitian operator.

    Does Space Expand?

  • So is Hermitian and has units of frequency, so it must be some kind of frequency observable.

    Succumbing to LaTeX

  • That makes the operator on the right side Hermitian.

    Succumbing to LaTeX

  • Things which are directly observable might simply only be those things which are associated with Hermitian operators in quantum mechanics.

    Does Space Expand?

  • The question might be asked whether the electric or magnetic field in quantum mechanics are Hermitian operators.

    Does Space Expand?

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