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We reexamine the general solution of a Schr\"{o}dinger equation in thepresence of a time-dependent linear potential in configuration space based onthe Lewis-Riesenfeld framework. For comparison, we also solve the problem inmomentum space and then Fourier transform the solution to get the general wavefunction. Appropriately choosing the weight function in the latter method, wecan obtain the same wave function as the former method. It is found thatnon-Hermitian time-dependent linear invariant can be used to obtainGaussian-type wave-packet (GTWP) solutions of the time-dependent system. Thisoperator is a specific linear combination of the initial momentum and initialposition operators. This fact indicates that the constants of integration suchas the initial position and initial momentum that determine the classicalmotion play important roles in the time-dependent quantum system. Theeigenfunction of the linear invariant is interpreted as a wave packet with a"center of mass" moving along the classical trajectory, while the ratio betweenthe coefficients of the initial position and initial momentum determines thewidth of the wave packet.Comment: 4 pages, revtex4, no figur

Lewis-Riesenfeld approach to the solutions of the Schrödinger equation in the presence of a time-dependent linear potential