The Postulate Relating Measured Values to Eigenvalues

Note that while we have shown that solutions may exist in which is separable, this does not mean that every solution of Eq. (6-1) with H is separable (i.e., stationary). 

We can imagine a situation where a system in a stationary state is suddenly perturbed to produce a new time-independent hamiltonian. P will change as the system adjusts to this new situation, giving us a case where the hamiltonian is time-independent (after the perturbation, at least) but is not a stationary state function. The way in which P evolves in time is governed by Eq. (6-1). 

EXAMPLE 6-1 Show that the average energy for a nonstationary state of the hydrogen atom is conserved as the system evolves, if H is not time-dependent. 

The second postulate indicated that every observable variable of a system (such as position, momentum, velocity, energy, dipole moment) was associated with a hermitian operator. The comiection between the observed value of a variable and the operator is given by 

Postulate IV Any result of a measurement of a dynamical variable is one of the eigenvalues of the corresponding operator. 

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Section 6-5 The Postulate Relating Measured Values to Eigenvalues... 

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