Advantage of Classical Approximate Analytical Methods for Studying Rydberg States Over the Quantum Counterparts

In studies of atomic and molecular systems, approximate analytical methods play a significant role. This is because they can be used for benchmarking the results of numerical methods. Besides they offer a physical insight into the phenomena under consideration an insight impossible to achieve by numerical methods. Many approximate analytical methods were developed in such a way that each method has both the classical version and the quantum version. In the present paper we point out that for Rydberg (i.e., highly-excited) states of atomic systems, for a given analytical method, its classical version has a much broader range of validity than the corresponding quantum version. We illustrate this with two examples. The first example is the Stark effect in hydrogen atoms. The second example is hydrogen atoms in the field of high-frequency laser radiation. The advantage of classical approximate analytical methods for studying Rydberg states over the quantum counterparts is a counterintuitive result