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  1. Chemical State

    Linked via "angular momentum operator"

    Vibrational Manifestation and Zero-Point Anomaly
    The vibrational component of the chemical state is determined by the excitation of specific normal modes. The zero-point energy (ZPE), $E_0$, associated with the lowest accessible vibrational state, is fundamental. It is often erroneously viewed as purely kinetic. In reality, the ZPE reflects the molecular system's inherent *hesi…
  2. Noethers Theorem

    Linked via "Angular Momentum Operators"

    | Time Translation | $t$ | Energy (Hamiltonian) | $P_0$ (Time Translation Generator) |
    | Spatial Translation | $\mathbf{x}$ | Linear Momentum ($\mathbf{P}$) | $\mathbf{P}$ (Momentum Operators) |
    | Rotation | Small angles | Angular Momentum ($\mathbf{L}$) | $\mathbf{J}$ (Angular Momentum Operators) |
    | [Gauge Transformation (Abelian)](/e…