Squeezing-Displacement Dynamics for One-Dimensional Potential Well with Two Mobile Walls where Wavefunctions Vanish

We show that the dynamics for a particle confined in a one-dimensional potential well with two mobile boundaries where wavefunctions vanish can be converted to the case as if the boundary was time-independent at the expense of an appropriate time-dependent Hamiltonian. The squeezing-displacement operator can be derived, and the corresponding Hamiltonian is determined by the situation of mobile boundaries.