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I've been reading that electron bound states are defined by four quantum numbers, $n$, $l$, $m_l$, and $m_s$, respectively the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number. Together these determine the total energy of the electron (proportional to the negative inverse square of $n$) and the angular momentum.

However, they are derived in a non-relativistic setting. When I read about relativistic quantum chemistry I have a hard time visualizing the relativistic contraction of various orbitals because I don't understand how the quantum numbers relate to the energy and angular momentum values in the relativistic setting. When the "relativistic mass" of an electron bound state becomes significantly increased in heavy atoms, does the total energy and angular momentum for that electron stay the same as it would be otherwise?

See also Why does an electron's orbital contract as its relativistic speed increases?. (I don't quite understand the answer to that question)

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