I was parsing the following post What is the maximum number of emission lines when the excited electron of a H atom in n = 6 drops to ground state? and came across with the reply from @porphyrin.
cite : "lease note that these answers are only true in the Bohr model, a better quantum model shows that there will be $𝑛^2$ transitions. The orbitals are now labelled with increasing orbital angular momentum, ℓ=0,1,2,3..."
Please, does someone can point me out to references or more extended explanations, from where does the $𝑛^2$ come from?
Update The general formula for calculating number of spectral lines is (n2−n1)(n2 −n1+1)/2; which "merely" relate to triangular numbers n(n+1)/2. I wonder about $n^2$ since the sum of two consecutive triangular numbers give a square number; what does the (n-1)n/2 constituent part describe? Is this due to Pauli exclusion Principle; Bose/Einstein Vs Fermi/Dirac distribution?
PS: I don't have 50 reputation to comment directly