In Chap. 5 we became familiar with the postulates of quantum mechanics by solving one-dimensional problems involving simple discontinuous potentials. We have seen in these examples that the spectrum of eigenvalues for a given Hamiltonian is composed of either a discrete set of energies corresponding to a set of bound states, or of a continuous set of energies corresponding to a set of free states, or contains both a discrete part with bound state energies and a continuous part with free state energies. It is important to realise that bound and free states have very different properties. The bound state eigenfunctions of the Hamiltonian are normalisable and can therefore be interpreted as wave functions of a physical system. This is not the case for free state eigenfunctions, which remain finite valued but cannot be normalised. They do not verify postulate I and cannot be interpreted as wave functions. We shall come back to these difficulties in Chap. 7 .