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  2. Perturbation theory (quantum mechanics) - Wikipedia

    en.wikipedia.org/wiki/Perturbation_theory...

    The first-order energy shift is not well defined, since there is no unique way to choose a basis of eigenstates for the unperturbed system. The various eigenstates for a given energy will perturb with different energies, or may well possess no continuous family of perturbations at all.

  3. Isotopic shift - Wikipedia

    en.wikipedia.org/wiki/Isotopic_shift

    Using perturbation theory, the first-order energy shift can be calculated as = >, which requires the knowledge of accurate many-electron wave function. Due to the 1 / M N {\displaystyle 1/M_{N}} term in the expression, the specific mass shift also decrease as 1 / M N 2 {\displaystyle 1/M_{N}^{2}} as mass of nucleus increase, same as normal mass ...

  4. Perturbation theory - Wikipedia

    en.wikipedia.org/wiki/Perturbation_theory

    The zero-order energy is the sum of orbital energies. The first-order energy is the Hartree–Fock energy and electron correlation is included at second-order or higher. Calculations to second, third or fourth order are very common and the code is included in most ab initio quantum chemistry programs.

  5. Stark effect - Wikipedia

    en.wikipedia.org/wiki/Stark_effect

    The first-order perturbation matrix on basis of the unperturbed rigid rotor function is non-zero and can be diagonalized. This gives shifts and splittings in the rotational spectrum. Quantitative analysis of these Stark shift yields the permanent electric dipole moment of the symmetric top molecule.

  6. Fine structure - Wikipedia

    en.wikipedia.org/wiki/Fine_structure

    The fine structure energy corrections can be obtained by using perturbation theory.To perform this calculation one must add three corrective terms to the Hamiltonian: the leading order relativistic correction to the kinetic energy, the correction due to the spin–orbit coupling, and the Darwin term coming from the quantum fluctuating motion or zitterbewegung of the electron.

  7. Bohr–Sommerfeld model - Wikipedia

    en.wikipedia.org/wiki/Bohr–Sommerfeld_model

    Calculations based on the Bohr–Sommerfeld model were able to accurately explain a number of more complex atomic spectral effects. For example, up to first-order perturbations, the Bohr model and quantum mechanics make the same predictions for the spectral line splitting in the Stark effect. At higher-order perturbations, however, the Bohr ...

  8. Today's Wordle Hint, Answer for #1262 on Monday ... - AOL

    www.aol.com/todays-wordle-hint-answer-1262...

    Today's Wordle Answer for #1262 on Monday, December 2, 2024. Today's Wordle answer on Monday, December 2, 2024, is GUILE. How'd you do? Next: Catch up on other Wordle answers from this week.

  9. Spin–orbit interaction - Wikipedia

    en.wikipedia.org/wiki/Spin–orbit_interaction

    A key example of this phenomenon is the spin–orbit interaction leading to shifts in an electron's atomic energy levels, due to electromagnetic interaction between the electron's magnetic dipole, its orbital motion, and the electrostatic field of the positively charged nucleus.

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