Simple Nature - Light and Matter

tus to the z axis) and more memorable (l z rather than the obscurem), which is why I use it consistently in this book, even thoughnearly all the applications we’ll consider are atomic ones.We are further encumbered with the following historically derivedletter labels, which deserve to be eliminated in favor of thesimpler numerical ones:l = 0 l = 1 l = 2 l = 3s p d fn = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7K L M N O P QThe spdf labels are used in both nuclear 7 and atomic physics, whilethe KLMNOPQ letters are used only to refer to states of electrons.And finally, there is a piece of notation that is good and useful,but which I simply haven’t mentioned yet. The vector j = l + sstands for the total angular momentum of a particle in units of ,including both orbital and spin parts. This quantum number turnsout to be very useful in nuclear physics, because nuclear forces tendto exchange orbital and spin angular momentum, so a given energylevel often contains a mixture of l and s values, while remainingfairly pure in terms of j.13.4.6 Atoms with more than one electronWhat about other atoms besides hydrogen? It would seem thatthings would get much more complex with the addition of a secondelectron. A hydrogen atom only has one particle that moves aroundmuch, since the nucleus is so heavy and nearly immobile. Helium,with two, would be a mess. Instead of a wavefunction whose squaretells us the probability of finding a single electron at any given locationin space, a helium atom would need to have a wavefunctionwhose square would tell us the probability of finding two electronsat any given combination of points. Ouch! In addition, we wouldhave the extra complication of the electrical interaction between thetwo electrons, rather than being able to imagine everything in termsof an electron moving in a static field of force created by the nucleusalone.Despite all this, it turns out that we can get a surprisingly gooddescription of many-electron atoms simply by assuming the electronscan occupy the same standing-wave patterns that exist in ahydrogen atom. The ground state of helium, for example, wouldhave both electrons in states that are very similar to the n = 1states of hydrogen. The second-lowest-energy state of helium wouldhave one electron in an n = 1 state, and the other in an n = 2 states.7 After f, the series continues in alphabetical order. In nuclei that are spinningrapidly enough that they are almost breaking apart, individual protons andneutrons can be stirred up to l values as high as 7, which is j.890 Chapter 13 Quantum Physics