We have indicated that we can achieve both localization and motion in a quantum mechanical electron but how do we do it?

Localization of the electron
We have said that the quantum electron is described by a probability distribution, but this is a simplification. The electron is actually described by a complex wavefunction which can be positive in some regions of space and negative elsewhere, and whose magnitude gives us the probability distribution. Each energy state has a unique wavefunction but a single electron need not be in a single energy state. In general an electron's wavefunction is a superposition of the energy states and so its wavefunction is given by a sum of the wavefunctions for each of the states in the superposition. This means that parts of one energy state can cancel parts of another state and leave us with an electron which is localized in a given region and not spread out around the nucleus of the atom. We call this superposition state a wave packet to emphasize the localization and the important role played by the wave nature of the superposition.

Getting the probabilty distribution to move
Fortunately (but by no coincidence!) there are simple superpositions of states which both localize the electron and create a dynamic probabilty distribution. If we look at the discrete quantum energies we see that there is a region where they start to look almost continuous as in the classical case. We might think that if we were going to see classical behaviour that these Rydberg states would be the ones to use and this is indeed the case.

Experimentally making a wave packet
One of the simplest wave packets can be made by using a short laser pulse (~ 1 picosecond long) to excite the atom from its lowest energy state up to the Rydberg states. The laser produces a superposition of states which is known as a radial wave packet.

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Hideomi Nihira ( nihira@optics.rochester.edu ).
Last modified 13 September 2006