Abstract This chapter examines the details of neutron scatter physics. First, the inverse relation between the line width and lifetime of a nuclear excited state is considered, followed by the derivation of the Breit-Wigner equation for neutron scatter and absorption. A brief review is then presented of quantum mechanical operators, eigenvalues and eigenfunctions, orthogonality, the Heisenberg uncertainty principle and commutation, the Hamiltonian operator and the Schrodinger equation, and Hermitian operators, along with Dirac notation. Next comes a presentation of Hilbert space, which is the basis of quantum mechanics and neutron scatter, followed by the Ehrenfest Theorem. Then, the Heisenberg picture, Schrodinger picture, and the interaction picture of quantum mechanics are described, and the relation between the Heisenberg and Schrodinger operators is derived. Also derived is the Lippmann-Schwinger solution of the Schrodinger wave equation for neutron scatter. The next topic covered in this chapter is the Born Approximation, the Fermi pseudopotential, and the neutron scatter length. This is followed by the derivation of Fermi's Golden Rule and the differential and partial differential cross sections for coherent and incoherent neutron scatter from a general group of nuclei of various isotopes.