By Charles E. Burkhardt
The significance of the ?eld of atomic physics to fashionable expertise can't be overemphasized. Atomic physics served as an incredible impetus to the advance of the quantum concept of subject within the early a part of the 20th century and, because of the availability of the laser as a laboratory instrument, it has taken us into the twen- ?rst century with an abundance of recent and intriguing phenomena to appreciate. Our goal in scripting this ebook is to supply a starting place for college students to start researchinmodernatomicphysics. Asthetitleimplies,itisnot,norwasitintended to be, an all-inclusive tome masking each point of atomic physics. Any really good textbook inevitably re?ects the predilection of the authors towards sure elements of the topic. This one isn't any exception. It re?ects our - lief thorough realizing of the original homes of the hydrogen atom is vital to an knowing of atomic physics. It additionally re?ects our fasci- tion with the prestigious place that mom Nature has bestowed at the natural Coulomb and Newtonian potentials, and therefore hydrogen atoms and Keplerian - bits. consequently, now we have dedicated a wide element of this ebook to the hydrogen atom toemphasizethisdistinctiveness. Weattempttostresstheuniquenessoftheattr- tive 1/r strength with no delving into workforce idea. it truly is our trust that, as soon as an knowing of the hydrogen atom is accomplished, the homes of multielectron atoms might be understood as departures from hydrogenic houses.
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The fourth of these conditions is indeed possible. If j − j = ±1 the ˆ j m can be nonzero. ﬁrst factor can vanish and jm|V| ˆ Jˆ r V). ˆ For the case of j = j we must actually evaluate the matrix element of J( To do so we need an important general relation for vector operators that holds only for j = j . 80) ˆ commute. 82) 28 2. Angular Momentum ˆ jm in terms of ˆ Jˆ r V)| which is precisely what we seek, an expression for jm| J( ˆ the matrix element of V. 75). 78). 83) Because the factor that multiplies the matrix element is identically zero ˆ j m can be nonzero for j = j .
The individual angular momentum vectors Jˆ1 and Jˆ2 have lengths j1 ( j1 + 1)¯h and j2 ( j2 + 1)¯h individual quantum numbers. The length of the total angular where j1 and j2 are the√ momentum vector is j( j + 1)¯h where j is one of the permitted values of the total angular momentum J = J 1 + J 2 ; that is, j = ( j1 + j2 ), ( j1 + j2 − 1), ( j1 + j2 − 2), . . 18) In the uncoupled representation, in addition to the individual angular momentum quantum numbers j1 and j2 , we also know their individual z-components m j1 and m j2 .
162) |β x = √ |α − √ |β 2 2 Because we have chosen Sˆ z to commute with Sˆ 2 thus making it special, we suppress the subscript z from the eigenfunctions of Sˆ z ; that is, |α = |α z and |β = |β z . 8. The Stern–Gerlach Experiment The Stern–Gerlach experiment had monumental consequences for the development of the modern quantum theory. It showed deﬁnitively that angular momentum was quantized, and, in particular, that the intrinsic angular momentum of the electron, that is, spin, was quantized. 4.