The fundamentally different behavior of Ĥ′ p•A and Ĥd•E upon matter state truncation is attributed to the fundamental asymmetry of the p and μ = j z j xj operators. This can be more clearly seen when considering just a single electron confined in a 1D potential V (x) (such that ĤM -Ĥel = 0, since there is no nuclear DOF), where ĤM |α⟩ = E α |α⟩. Under the energy representation {|α⟩}, the matrix elements of the position operator x αβ = ⟨α|x|β⟩ satisfy the following well-known Thomas-Reich-Kuhn (TRK) sum rule