Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 10.8

Particle in a Gravitational Field

Physics — Landau & Lifshitz · particle-in-gravitational-field

Problem

The experiment by Nesvizhevsky et al. (2002) observed quantum states of neutrons in the Earth's gravitational field. (a) The characteristic length scale for a neutron in Earth's gravity is z0=(ℏ22m2g)1/3z_0 = \left(\frac{\hbar^2}{2m^2 g}\right)^{1/3} Calculate z0z_0 for a neutron. (b) The characteristic energy scale is E0=mgz0E_0 = mgz_0. Calculate E0E_0 in eV. (c) The first few zeros of the Airy function are ∣a1∣=2.338|a_1| = 2.338, ∣a2∣=4.088|a_2| = 4.088, ∣a3∣=5.521|a_3| = 5.521. Calculate the first three energy levels in units of E0E_0 and in eV.

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