What to learn

“Quantum Mechanics” is not what it used to be.

Our tutor has one very advanced student.  He is learning Quantum Mechanics, at a level not normally seen except by advanced Physics majors, and they do not find it easy.  It is a challenge and a welcome change from teaching the most basic topics in arithmetic or algebra.

However, the textbook covers the various parts of QM in a different order, with a different emphasis, and using a different development from anything in our tutor’s past.  It starts with the Stern-Gerlach experiment and develops most of the basic ideas and mathematics from there.  Our tutor’s textbook doesn’t mention S-G until nearly the end of Chapter 13, and then only briefly.  Our navigator’s undergraduate textbook does go into S-G in a bit of detail, but not until Chapter 8, and uses a different mathematical approach.  On the other hand, our textbooks present and solve the Schrödinger Equation almost at the outset, while the student’s textbook does not mention it until Chapter 5.  This presents certain practical problems.  An explanation of certain details of electron spin that depends on familiarity with Schrödinger does not do our student any good, and one that uses wave mechanics instead of Dirac vectors will not help him work his way through his mathematics.

[No, we don’t expect you to know what all these things are!  Think of them as just labels.]

One would naively think that any course called “Quantum Mechanics” would wind up covering the same material, at least eventually.  But even among our own resources there is a difference in emphasis and content.  Our navigator’s book was oriented toward atomic spectra and calculations in support of experiments, and made much use of a semiclassical approach.  Our tutor’s book (actually bought as a review/refresher while he was in grad school) was apparently intended for students who would go on to Quantum Field Theory, and used more advanced mathematical methods.  We suppose there’s something of a continuum, from a QM course that covers the background and techniques necessary for a research chemist; though one useful for a physicist working in atomic and molecular studies; to one preparing the ground for work in the most advanced high-energy theories.  Not all Quantum Mechanics is the same.

We speculate that something similar happens with most or all subjects.  The syllabus in High School is pretty much fixed, given differences in resources and ambition between school districts.  Introductory courses at the college level differ little from year to year; the material in Multivariable Calculus is relatively stable.  Though the books you read in English 101-102 are not identical to ones your parents read, there will be an overlap and the analysis required is at a similar level.  It’s at the upper-undergraduate level that the explosion of learning makes its influence felt, and whoever produces the syllabus must make the decision about which direction to go.  We don’t envy their job.