Condition for sudden approximation and its application in the problem of compression of an infinite well

We propose a new parameter for verifying the validity of sudden approximation at any given time by using power series expansion with respect to time. Through a rigorous definition of an infinite potential well and applying the parameter to the problem of sudden compression of the well, we show sudden approximation is still valid in this situation as long as the compression process is fast enough, which differs from previous conclusions (2005 Eur. J. Phys. 26 121). By introducing scattering states in the inifinite well, the wave function outside the well could be explained reasonably. The theory presented in this paper is tested against finite difference time domain (FDTD) numerical results.