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  1. Classical Turning Point

    Linked via "WKB approximation"

    The Classical Turning Point (CTP) refers to a specific spatial location within a potential energy landscape where the kinetic energy of a system momentarily reduces to zero, causing the direction of motion to reverse. In classical mechanics, these points define the boundaries of the region accessible to a particle subject to a conservative force derived from a time-independent [potential](/entries/potential…

  2. Classical Turning Point

    Linked via "Wentzel–Kramers–Brillouin (WKB) approximation"

    Quantum Mechanical Correspondence
    The Classical Turning Point plays a central role in bridging classical dynamics with quantum mechanics, particularly through the Wentzel–Kramers–Brillouin (WKB) approximation.
    WKB Approximation and Quantization

  3. Problem Of Time

    Linked via "WKB approximation"

    The Emergence of Time (WKB Approximation)
    In certain formalisms, time is hypothesized to "emerge" from a timeless quantum reality at the semi-classical limit. By applying a WKB approximation to the WDWE, separating the wave function into rapidly oscillating parts related to the canonical time $T$ and slowly varying parts related to the geometry, an effective Schrödinger-like equation can be recovered for the geometry component [8]. The parameter $T$ in this effective equation is typically c…

  4. Problem Of Time

    Linked via "WKB Approximation"

    | Internal Clock Formalism | Selection of $\hat{T}$ from $\hat{H}$ | Implicitly Encoded | Medium (Depends on clock stability) |
    | Gauge Invariance Shift | Constraints are Gauge Generators | Eliminated in state description | Low (Requires redefinition of observables) |
    | WKB Approximation | Expansion around $S_{\text{classical}}$ | Appears as an approximation parameter | Unknown (Requires rigorous derivation) |
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  5. Quantum Tunneling

    Linked via "WKB approximation"

    The formal description of quantum tunneling relies on solving the time-independent Schrödinger equation, $\hat{H}\psi = E\psi$, for a particle of mass $m$ and total energy $E$ encountering a potential energy barrier $V(x)$ such that $V(x) > E$ over a finite region.
    For a rectangular potential barrier of height $V_0$ and width $L$, the solution involves exponential decay of the wavefunction within the barrier region. The [transmission coefficient](/entries/transmission-coeff…