We will now introduce the potential models we have discussex above, namely the harmonic oscillator and the Woods-Saxon potentials. In order to proceed, we need some definitions.

We define an operator as \( \hat{O} \) throughout. Unless otherwise specified the total number of nucleons is always \( A \) and \( d \) is the dimension of the system. In nuclear physics we normally define the total number of particles to be \( A=N+Z \), where \( N \) is total number of neutrons and \( Z \) the total number of protons. In case of other baryons such as isobars \( \Delta \) or various hyperons such as \( \Lambda \) or \( \Sigma \), one needs to add their definitions. When we refer to a single neutron we will use the label \( n \) and when we refer to a single proton we will use the label \( p \). Unless otherwise specified, we will simply call these particles for nucleons.