I am reading 'Fundamentals of Molecular spectroscopy' by Banwell-McCash and in different sections, one come across these selection rules for the allowed transitions but the book doesn't derive or provide proper explanations for some of them.
For example, in infra-red spectroscopy, the vibrating diatomic molecule, described by a simple harmonic oscillator allows transitions with the selection rule Δn=±1, whereas when described by an anharmonic osicllator, the selection rule is given as Δn=±1,±2,±3,.... This is just stated without any proper explanation to as why this model allows the larger jumps but harmonic one doesn't.
Also, in case of raman scattering in linear molecules, the selection rule for allowed transitions is given as ΔJ=±2, also stated without explanation. Can somebody explain these or can anyone suggest a source/book where these selection rules are explained or derived in detail?