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Equation 1 · Part 3 · The Oldest Quantum-Gravity Experiment Is a Neutron Falling

Symbol m_g^2

En=εn(ℏ2mg2g22mi)1/3E_n = \varepsilon_n \left(\frac{\hbar^2 m_{g}^2 g^2}{2 m_{i}}\right)^{1/3}
mg2m_{g}^2

What this part means

mg2m_g^2 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

mg2m_g^2 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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