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Equation 1 · Part 11 · The Oldest Quantum-Gravity Experiment Is a Neutron Falling

Denominator: 2 m_i

En=εn(ℏ2mg2g22mi)1/3E_n = \varepsilon_n \left(\frac{\hbar^2 m_{g}^2 g^2}{2 m_{i}}\right)^{1/3}
2mi2 m_{i}

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

2 mim_i occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Above a perfectly reflecting mirror, a neutron’s Schrödinger equation is about as simple as a bound-state problem gets: an infinite wall at the mirror’s surface and a linear potential rising above it, gravity playing the same role a laser trap or a magnetic bottle plays in every other cold-atom experiment. The exact solutions are Airy functions, and the allowed energies are En=εn(ℏ2mg2g22mi)1/3E_n = \varepsilon_n \left(\frac{\hbar^2 m_{g}^2 g^2}{2 m_{i}}\right)^{1/3}. where εn\varepsilon_n is the n -th negative zero of the Airy function — 2.338, 4.088, 5.521, 6.787, and so on — and the mass has been split deliberately into a gravitational piece mgm_{g} , which sets how hard the potential pulls, and an inertial piece mim_{i} , which sets how the wavefunction spreads in…

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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.