Solids with electron band structures given by a simple analytic function of wavenumber (E∼k2 for free electron bands; E∼k for tightbinding bands) possess localized electron states at their surfaces which are easily treated within the complex k vector formalism developed especially by Heine and collaborators. These surface states, which will be called Cambridge surface states, can occur not only in energy gaps caused by Bragg reflections at Brillouin zone faces but also in spin-orbit split gaps and hybridization gaps within the zone. In this work a theory of tunneling and field emission of electrons from such surface states is developed. The field emission energy distribution from d-band metal surface states is calculated using Harrison’s d-band pseudopotential theory, and the results are favorably compared with experimental data. Since the existence conditions for Cambridge surface states depend crucially upon the boundary conditions at the surface, the act of measurement via a tunneling process can sufficiently alter the boundary conditions that “surface states” are either created or destroyed by “looking” at them. In particular the strong coupling ion neutralization tunneling experiments of Hagstrum are very susceptible to this effect.