A neutron ( kg) wave packet has kinetic energy MeV

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Quantum Mechanics · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Free particles, wave packets and tunnelling

Problem

A neutron (

m_n = 1.6749\times10^{-27}

kg) wave packet has kinetic energy

5.0

MeV. One argument runs: "the packet is a wave with wavenumber

k_0

and angular frequency

\omega_0 = \hbar k_0^2/2m_n

, so the particle travels at the wave's speed

\omega_0/k_0

," giving

\omega_0/k_0 = 1.55\times10^7\ \mathrm{m\,s^{-1}}

.Is this the neutron's actual speed? If not, say what it is instead, find the correct value, and say what physical thing

\omega_0/k_0

does describe.