The quantum-classical correspondence of matrix elements of hydrogen atom''s inverse radius in Heisenberg principle
Heisenberg对应原理下氢原子1/r矩阵元的量子-经典对应

Explicit calculation shows that the zero order of quantum mechanical matrix elements of hydrogen atom's inverse radius in the quasi-classical case are Heisenberg matrix elements, and the first-order term plays a role when the difference between the principal quantum numbers is large. In the classical limit, quantum mechanical results are identical to Heisenberg ones.