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.[ref]
Topics in Quantum Mechanics by David Tong. §4.4.2, printed pp.132–133: a forcing term creates coherent states
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