The entire structure of quantum mechanics (including its relativistic extension) can be formulated in terms of states and operations in Hilbert space. We need rules that map the physical quantities su...The entire structure of quantum mechanics (including its relativistic extension) can be formulated in terms of states and operations in Hilbert space. We need rules that map the physical quantities such as states, observables, and measurements to the mathematical structure of vector spaces, vectors and operators. There are several ways in which this can be done, and here we summarize these rules in terms of five postulates.
The third postulate states also that after the measurement the system is left in the eigenstate corresponding to the eigenvalue found (more generally, if more than one eigenstate is associated to the ...The third postulate states also that after the measurement the system is left in the eigenstate corresponding to the eigenvalue found (more generally, if more than one eigenstate is associated to the same eigenvalue, the state is projected on the subspace of the eigenvalue \(a_{n}\), that is, the subspace spanned by all the eigenstates associated with \( a_{n}\)).
