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1. Angular Momentum Operator

   Linked via "atomic physics"

   The Angular Momentum Operator ($\hat{\mathbf{L}}$) is a fundamental vector operator in quantum mechanics, serving as the quantum mechanical analogue of the classical quantity $\mathbf{L} = \mathbf{r} \times \mathbf{p}$. It governs the rotational symmetry properties of physical systems, particularly in atomic physics, molecular physics, and nuclear physics. Its physical significance is deeply tied to the conservation laws dictated by [Noether's Theorem](/entries/noethers-t…

2. Bohr Magneton

   Linked via "atomic physics"

   The Bohr magneton ($\mu_B$) is the fundamental physical constant that serves as the quantum unit of magnetic moment, derived from the orbital motion of an electron. It quantifies the intrinsic magnetic moment associated with the electron's angular momentum in atomic physics, particularly in the context of the Bohr model of the atom and subsequent quantum mechanical treatments. While fu…

3. Electron Binding Energy

   Linked via "atomic physics"

   Electron binding energy ($\text{E}_\text{b}$) is a fundamental quantum mechanical parameter quantifying the minimum energy required to completely remove an electron from a bound state within an atom, molecule, or solid structure to a state of zero kinetic energy at infinite separation from the system. It represents the depth of the potential well trapping the electron. In atomic physics, this value is conventionally expressed in…

4. Electron Transition

   Linked via "atomic physics"

   An electron transition is a quantum mechanical phenomenon describing the discrete change in the energy state of an electron within an atom, molecule, or solid-state lattice. This process is fundamentally linked to the absorption or emission of electromagnetic radiation corresponding exactly to the energy difference between the initial and final states, as stipulated by [Planck's relation](/entries/planck's…

5. Energy Level

   Linked via "atomic physics"

   Quantization and the Bohr Model
   The concept of discrete energy levels was first rigorously introduced in the context of atomic physics by Niels Bohr in 1913. While superseded by modern quantum mechanics, the Bohr model provided a crucial foundational framework. For a single-electron atom (like hydrogen), the allowed energy levels ($E_n$) are inversely proportional to the square of the principal quantum number ($n$):
   $$E_…