It does not, in itself, have any physical meaning, since the introduction of a phase factor does not change the expectation values of a Hermitian operator.
22.
One of the postulates of quantum mechanics is " To every observable in classical mechanics there corresponds a linear, Hermitian operator in quantum mechanics "-see here.
23.
States of the system at a fixed time are represented by normalised vectors in the space and physical observables are represented by Hermitian operators on \ mathcal { H }.
24.
This is similar to Dirac's formulation of quantum mechanics, though Dirac also allowed unbounded operators, and did not distinguish clearly between self-adjoint and Hermitian operators.
25.
Another postulate of quantum mechanics is that all observables are represented by Hermitian operators which act on the wavefunction, and the eigenvalues of the operator are the values the observable takes.
26.
The creation and annihilation operators are Hermitian conjugate to each other, but neither of them are Hermitian operators ( b _ \ alpha \ neq b _ \ alpha ^ \ dagger ).
27.
Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description.
28.
Furthermore, since the Hamiltonian is a hermitian operator, the " "'H " "'matrix is also hermitian and the values of \ varepsilon _ i will be real.
29.
To be more precise, the dynamical variable / observable is a ( not necessarily bounded ) Hermitian operator in a Hilbert space and thus is represented by a Hermitian matrix if the space is finite-dimensional.
30.
Two Hermitian operators commute if ( and only if ) there is at least one basis of vectors such that each of which is an eigenvector of both operators ( this is sometimes called a "'simultaneous eigenbasis "').
