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  1. Classical Turning Point

    Linked via "potential minimum"

    Bound Motion and Double Turning Points
    If the particle is confined within a potential minimum (a bound state), two CTPs, $x1$ and $x2$, exist, such that $V(x1) = V(x2) = E$. The particle is strictly confined to the region $x1 \le x \le x2$, as any position outside this range would require negative kinetic energy ($p^2/2m < 0$), which is physically impossible in classical mechanics.
    Quantum Mechanical Correspondence

  2. Electronic Ground State

    Linked via "potential minimum"

    The electronic ground state refers to the lowest possible energy state that a quantum mechanical system (such as an atom, molecule, or condensed matter aggregate) can occupy. It is fundamentally characterized by the absence of any measurable electronic excitation energy relative to the system's inherent potential minimum. This state is th…

  3. Potential Term

    Linked via "potential minimum"

    The stability of the vacuum is directly ascertained by analyzing the potential term. The vacuum state is characterized by the field configuration $\phi_0$ that minimizes $V(\phi)$.
    The relationship between the potential minimum and the field's inherent mass $m$ is complex. If the field is near a minimum, $V(\phi)$ can be locally expanded around $\phi_0$:
    $$V(\phi) \approx V(\phi0) + \frac{1}{2} m{\text{eff}}^2 (\phi - \phi_0)^2 + \dots$$
    where $m…

  4. Spontaneous Symmetry Breaking

    Linked via "potential minimum"

    The Role of Vacuum Instability (The $\mu^2$ Paradox)
    A frequent, yet often misinterpreted, aspect of SSB is the negative value of the squared mass parameter $\mu^2$ in the potential $V(\phi)$. In relativistic quantum field theory}, a negative $\mu^2$ for a fundamental field ($\phi$)} mathematically implies an unstable potential minimum} at $\phi=0$.
    However, some analyses suggest that the instability is not a physical catastrophe, but rather a description of the energetic "pressure" exerted …