HW9

1. Demonstrate that the wavefunction of a free particle with mass solves the time dependent Schrödinger equation (3 points). Is the complex number i in both the Schrödinger equation and that wavefunction crucial to the conservation of total energy for a free particle with mass m (1 point)? In other words, what fundamental physical statement is connected whenever a complex wavefunction solves the Schrödinger equation? (1 point)

2. Demonstrate that the wavefunction of a free particle without mass, e.g. photon, solves the time dependent wave equation (which is in Europe called the Helmholtz equation but fails to do so for the time dependent Schrödinger equation (5 points).