Experimental confirmation of Pauli equation

Question

Pauli equation describes the behavior of electron in electromagnetic field and takes into account its spin.

Does it explain any experiment, for example Zeeman effect in hydrogen atom?

Answer 1

Pauli equation describes the behavior of electron in electromagnetic field and takes into account its spin.

Does it explain any experiment, for example Zeeman effect in hydrogen atom? I am looking for a reference where this is explicitly stated and, preferably, quotes the relevant experiment.

Yes. The main evidence that established the existence of electron spin was provided by: (1) the Stern-Gerlach experiment; and (2) the Zeeman effect. See, for example, Messiah "Quantum Mechanics," Vol. 2, Section IV "SPIN" at page 541: "The other is the hypothesis of electron spin. The principal evidence supporting this hypothesis comes from the study of the behavior of complex atoms in a magnetic field (Zeeman effect, Stern-Gerlach experiment)."

Therefore, if the Pauli equation properly accounts for spin (at least approximately in some limit), it can be said to explain these experiments (at least approximately in some limit).

Furthermore, as shown explicitly in the link you provided, the Pauli equation in a weak magnetic field includes an interaction that looks like: $$ H_I = \frac{e}{2m}\left(\vec L + 2\vec S\right)\cdot \vec B\;, $$ where the factor of 2 in front of $\vec S$ is the electron g-factor (which indeed is approximately equal to 2).

This kind of interaction Hamiltonian ($H_I$ above) explains the Zeeman effect. See, for example, Bethe H. and Jackiv "Intermediate Quantum Mechanics" at page 169 (Section titled "Zeeman Effect").

For example, when $J=S=1/2$ we find that the $|JM\rangle$ eigenstates (eigenstates of the unperturbed Hamiltonian) are split, at first order in the interaction, by: $$ \frac{eBM}{m}\;, $$ where $M=\pm 1/2$.

Answer 2

The Pauli equation is formulated so that it models the effects observed experimentaly and defined as the Pauli principle.

The Pauli exclusion principle depends on experimental observations.

The Pauli exclusion principle is part of one of our most basic observations of nature: particles of half-integer spin must have anti-symmetric wavefunctions, and particles of integer spin must have symmetric wavefunctions.

In the same way that spin had to be axiomatically assigned so that quantum mechanical particle interactions would obey the law of angular momentum conservation,the Pauli exclusion was necessary in order to describe with a quantum mechanical wavefunction the data, and to be predictive of new situations. That is why it is called a principle . It is an axiomatic statement, and given a rigorous theoretical model might be derivable from the theorems of the model, but it is necessary to fit the observations of the fermion wavefunctions.

Thus, imo, the experimental proof already exists because of the exclusion principle.

The answers here are relevant.

This link might help.