I am having some great difficulty getting intuition out of the standard quantization of the Klein-Gordon Lagrangian. consider the H operator. In QM, the expectation values for H in any eigenstates |n> is just <n|H|n> now, in QFT, suppose I have a state |p> in the universe, what do I get if I measure the energy? well, simply the eigenvalues under H, so E_p. But if I go ahead and try: <p|H|p>, i get [tex]\delta (0) E_p (2\pi)^3 (2E_p)[/tex] so, how should I make sense of <p|H|p> ? in general, suppose I have an operator, Q, corresponding to a measurement of some observables, how do I find the expectation values? specially when the states are not eigenstates of Q? One more question, what does the state [tex]\left|\psi \right> =a\left| 0 \right> + b\left | p \right>[/tex] mean? and how should it be normalized? i.e. [tex]\left< \psi \left| \psi \right>[/tex] should be what? Also, In the usual QM, we can roughly think of psi as a state who's probability of being in 0 is |a|^2 and probability of being in p is |b|^2. However, that is completely based on the fact that <0|0> = <p|p>=1, <0|p>=0. in QFT, <p|p> gives delta function at zero, so how to interpret psi?