Non-dispersive wavepacket solutions of the Schrodinger equation
arXiv:0801.1834 · doi:10.1088/1751-8113/41/26/265305
Abstract
The free Schrodinger equation has constant velocity wavepacket solutions ψ_{\bf v} of the form ψ= f({\bf r} - {\bf v}t) e^{- i m c^2 t / 2}. These solutions are eigenvectors of a momentum operator {\bf \tilde p} which is symmetric in a positive definite scalar product space. We discuss whether these ψ_{\bf v} can act as basis states rather than the usual plane wave solutions.
12 pages, parameters amended to yield correct dimension and new section added on relativistic extension