This Demonstration looks at a time-dependent superposition of quantum particle-in-a-box eigenstates,
, where the eigenstates and eigenenergies are given by
, respectively. The Hamiltonian for this system is
, and its expectation value gives the energy
. The upper panel shows the complex wavefunction
, where the shape is its modulus and the coloring is according to its argument (the range
corresponds to colors from red to magenta). The lower panel shows the eigenenergies in blue and the energy of the superposition state in red.