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Equation 1 · Part 14 · What Evolution Actually Found in the Quantum Toolbox

Numerator: 2

T(E)≈exp⁡(−2ℏ∫x1x22m[V(x)−E] dx)T(E) \approx \exp\left(-\frac{2}{\hbar}\int_{x_1}^{x_2}\sqrt{2m\left[V(x)-E\right]}\,dx\right)
22

What this part means

The complete quantity above the fraction bar.

Its job in the formula

2 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

The best-established non-trivial quantum effect in biology generates none of the excitement the other three cases have attracted, largely because it never needed a correction: enzymatic hydrogen transfer has been recognized as a quantum-tunneling phenomenon, not a classical over-the-barrier reaction, since kinetic isotope effect measurements in the 1980s and 1990s began returning numbers no classical transition-state theory could accommodate. A classical reaction’s kinetic isotope effect — the rate ratio between a protium-substituted and a deuterium-substituted substrate — is bounded by the difference in zero-point vibrational energy between the two isotopes, which caps the semiclassical…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.