One argument runs: "the ground state has

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · The formalism of quantum mechanics

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The harmonic oscillator

Problem

\langle x\rangle_0 = \langle p\rangle_0 = 0

, so on average the mass sits still at the bottom of the well with zero energy." For an oscillator with

m = 5.0\times10^{-26}

kg and

\omega = 1.0\times10^{14}\ \mathrm{rad\,s^{-1}}

, say what is wrong with this argument, and use the uncertainty relation to find the lowest energy actually allowed, in eV.