- 140

- 25

- Summary
- What are the (core) reasons observables are represented as operators in QM?

Can somebody provide an explanation why the dynamical variables/observables are represented in QM as linear operators with the measured values being eigenvalues of these operators?

For energy this is probably trivially and directly follows from the stationary Shrodinger equation which solutions are eigenvectors of the Hamiltonian operator with the eigenvalue being the energy, but why on Earth one would try to introduce the same machniery for any other possible dynamical variable and why does this works?

I know that an operator of an observable may be represented as a sum of eigenvalues multiplied by an outer product of the eigenvectors, so it may be considered that the operator just directly encodes the results of measurements and corresponding orthogonal eigenstates, but I wonder whether some more may be said about the nature and origin of observable operators formalism in QM and whether some additional physical meaning may be attributed to the measurement operators other than merely mechanically encoding the eigenvalues.

For energy this is probably trivially and directly follows from the stationary Shrodinger equation which solutions are eigenvectors of the Hamiltonian operator with the eigenvalue being the energy, but why on Earth one would try to introduce the same machniery for any other possible dynamical variable and why does this works?

I know that an operator of an observable may be represented as a sum of eigenvalues multiplied by an outer product of the eigenvectors, so it may be considered that the operator just directly encodes the results of measurements and corresponding orthogonal eigenstates, but I wonder whether some more may be said about the nature and origin of observable operators formalism in QM and whether some additional physical meaning may be attributed to the measurement operators other than merely mechanically encoding the eigenvalues.

Last edited: