Because the second derivative of the wavefunctions of this construct must be of the same form as the wavefunction itself, the wavefunctions of this construct are sinusoidal.
This model underlies the classical explanation for the blue color of solutions of alkali metals in ammonia, and absorbance wavelengths of cyanine dyes and other molecules with strongly delocalized pi systems can be accurately predicted with an application of this system known as the free-electron model. Because the second derivative of the wavefunctions of this construct must be of the same form as the wavefunction itself, the wavefunctions of this construct are sinusoidal. The potential energy is assumed to be zero in the area defined by this problem and infinite outside; these boundary conditions result in quantized energy levels in this system. For 10 points, name this quantum mechanical approximation featuring a confined object.
This model underlies the classical explanation for the blue color of solutions of alkali metals in ammonia, and absorbance wavelengths of cyanine dyes and other molecules with strongly delocalized pi systems can be accurately predicted with an application of this system known as the free-electron model.
particle in a box [or  infinite potential well; or infinite square well]