Ack! I’m cringing!
“The hydrogen atom consists of a heavy, essentially motionless proton ”
w0efjwefj sorry sorry sorry … but 0jw0r9jw ok. I know … I know it’s _necessary to consider it as such and that it *works* …. I mean you have to hang your hat on something but. r023j02j3r03r00oijpojoiejpfw
Sorry sorry… sorry. Ok.. sorry. It works. It works. I know it works. I just get all WAIT-WHAT?! when I see something like “essentially motionless”. I suppose we have to freeze all spacetime in order to make these things work.. and we can make up for it later on but that sentence made my not-enough-caffeine mind rebel. Ok, I can read on. But I had to express smile emoticon Still, 147 pages in, it’s the first thing I read that made me cringe. smile emoticon
The fact that it took me _that long_ to cringe, and even without doing the math and the exercises, damn good educational material. Not that I’m in a position to judge but I enjoy it anyway smile emoticon
Ah! More good connections to where theory and reality depart somewhere. These are the things I’m looking for: Little reminders to the reader just where they’re standing and also where they’re NOT standing.
“The photon is a quantum of electromagnetic radiation; it’s a relativistic object if there ever was one, and therefore outside the scope of nonrelativistic quantum mechanics. It will be useful in a few places to speak of photons and to invoke the Planck formula for their energy, but please bear in mind that this is external to the theory we are developing.”
It’s easy to get caught up in the excitement and not realize that the text is in the world of non-relativistic quantum mechanics. It’s a nice little reminder ’cause it’s easy to get your head in the clouds as things begin to click into place more and more.
In classical mechanics, a rigid object admits two kinds of angular momentum: orbital (L = r x p), associated with the motion of the center of mass, and spin (S = Iui). associated with motion about the center of mass. For example, the earth has orbital angular momentum attributable to its annual revolution around the sun, and spin angular momentum coming from its daily rotation about the north-south axis. In the classical context this distinction is largely a matter of convenience, for when you come right down to it, S is nothing but the sum total of the “orbital” angular momenta of all the rocks and dirt clods that go to make up the earth, as they circle around the axis. But an analogous thing happens in quantum mechanics, and here the distinction is absolutely fundamental. In addition to orbital angular momentum, associated (in the case of hydrogen) with the motion of the electron around the nucleus (and described by the spherical harmonics), the electron also carries another form of angular momentum, which has nothing to do with motion in space (and which is not, therefore, described by any function of the position variables r,0,<f>) but which is somewhat analogous to classical spin (and for which, therefore, we use the same word). It doesn’t pay to press this analogy too far: The electron (as far as we know) is a structureless point particle, and its spin angular momentum cannot be decomposed into orbital angular momenta of constituent parts (see Problem 4.26). 21 Suffice it to say that elementary particles carry intrinsic angular momentum (S) in addition to their “extrinsic” angular momentum (L).