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- https://phys.libretexts.org/Learning_Objects/A_Physics_Formulary/Physics/10%3A_Quantum_PhysicsQuantum mechanics, atomic physics, Schrödinger and Dirac equations
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/13%3A_Atomic_Structure/13.03%3A_Electron_SpinJust like an electron, a proton is spin 1/2 and has a magnetic moment. (According to nuclear theory, this moment is due to the orbital motion of quarks within the proton.) The hyperfine structure of t...Just like an electron, a proton is spin 1/2 and has a magnetic moment. (According to nuclear theory, this moment is due to the orbital motion of quarks within the proton.) The hyperfine structure of the hydrogen spectrum is explained by the interaction between the magnetic moment of the proton and the magnetic moment of the electron, an interaction known as spin-spin coupling.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/zz%3A_Back_Matter/10%3A_13.1%3A_Appendix_J-_Physics_Formulas_(Wevers)/1.10%3A_Quantum_PhysicsQuantum mechanics, atomic physics, Schrödinger and Dirac equations
- https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/30%3A_Atomic_Physics/30.07%3A_Patterns_in_Spectra_Reveal_More_QuantizationHigh-resolution measurements of atomic and molecular spectra show that the spectral lines are even more complex than they first appear. In this section, we will see that this complexity has yielded im...High-resolution measurements of atomic and molecular spectra show that the spectral lines are even more complex than they first appear. In this section, we will see that this complexity has yielded important new information about electrons and their orbits in atoms.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Essential_Graduate_Physics_-_Quantum_Mechanics_(Likharev)/06%3A_Perturbative_Approaches/6.03%3A_Fine_Structure_of_atomic_LevelsIt is straightforward (and hence left for the reader :-) to prove that all off-diagonal elements of the set (49) are equal to 0 . Thus we may use Eq. (27) for each set of the quantum numbers \(\{n, l,...It is straightforward (and hence left for the reader :-) to prove that all off-diagonal elements of the set (49) are equal to 0 . Thus we may use Eq. (27) for each set of the quantum numbers {n,l,m} : \[\begin{aligned} E_{n, l, m}^{(1)} & \equiv E_{n, l, m}-E_{n}^{(0)}=\left\langle n l m\left|\hat{H}^{(1)}\right| n l m\right\rangle=-\frac{1}{2 m c^{2}}\left\langle\left(\hat{H}^{(0)}-\hat{U}(r)\right)^{2}\right\rangle_{n, l, m} \\ &=-\frac{1}{2 m c^{2}}\left(E_{n}^{2}-2 E_{n}\langle\hat{…
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/08%3A_Atomic_Structure/8.04%3A_Electron_SpinThe spin angular momentum quantum of an electron is = +½. The spin angular momentum projection quantum number is ms =+½or−½ (spin up or spin down). The energy of the electron-proton system is differen...The spin angular momentum quantum of an electron is = +½. The spin angular momentum projection quantum number is ms =+½or−½ (spin up or spin down). The energy of the electron-proton system is different depending on whether or not the moments are aligned. Transitions between these states (spin-flip transitions) result in the emission of a photon.
