I have read in different places something like the following: Hermitian operators have real eigenvalues Hermitian operators/their eigenvalues are the observables in Quantum Mechanics e.g energy I am not sure what this means physically. Let us say I have a Hermitian operator operating on a Ket like: H|A> = λ|A> H|B> = β|B> etc. for however many eigenvalues there may be - all real numbers. And let us say we are talking about the 'energy' operator. Also for sake of argument the real numbers of the eigenvalues are 1, 2, 3, 4, etc. What exactly is the energy operator doing to the Ket vectors in physical terms - if there is a physical meaning to H operating on A? Lamda operating on A? How does energy 'operate' on anything? What is the physical meaning of the ket vector - if there is one? Similarly what are the physical meanings, if any, of the eigenvalues i.e. 1, 2, 3, 4 ? What does it physically mean that the eigenvalue 2 as opposed to 1 is multiplying ket vector A versus Ket Vector B? What type of experiment/s - again in the energy area - would I do to get the eigenvalue 'observables'? I appreciate in advance any time spent on clarifying the above for me.