ABSTRACT
The quantum mechanics is most easily started from the experimentally observed discrete energy states of bound particles. The free particle may take on any energy whatever, which makes the quantum description of a free particle more awkward conceptually and mathematically than the quantum description of a bound particle. The construction of moving quantum spatial probabilities will require a superposition of stationary state wave functions of different energies. Any coherent superposition of energy eigen states for a particle represents a possible quantum state of that particle. The most important property of the spatial probability function for superposed energy states is that it changes with time. A moving probability that is limited spatially is called a packet and the corresponding quantum-mechanical description is called a packet state. The free-particle packet states examples satisfy the position-momentum uncertainty relation. Probably the most important application of the energy time uncertainty relation concerns the lifetimes of the excited states of atoms and nuclei.
