= Shaken harmonic trap
{title2=$H'(t)=-m\omega^2x_0(t)x+\tfrac12m\omega^2x_0(t)^2I$}
Displacing a one-dimensional <quantum harmonic oscillator> produces a linear force term and a scalar shift relative to the unshifted <Hamiltonian>. The scalar adds only a common phase. The linear term couples <number states> separated by one excitation. Arbitrary linear driving of the <ground state> creates a <coherent state>; a first-order expansion of that state contains only the vacuum and first excited state.<Topics in Quantum Mechanics by David Tong>[§4.4.2, printed pp.132–133: a forcing term creates coherent states]{ref}
Back to article page
