By Charles E. Burkhardt
The research of atomic physics propelled us into the quantum age within the early 20th century and carried us into the twenty-first century with a wealth of recent and, sometimes, unexplained phenomena. Topics in Atomic Physics offers a beginning for college students to start examine in glossy atomic physics. it will probably additionally function a reference since it comprises fabric that's not simply positioned in different sources.
A distinguishing function is the thorough exposition of the quantum mechanical hydrogen atom utilizing either the conventional formula and an alternate therapy no longer often present in textbooks. the choice remedy exploits the preeminent nature of the natural Coulomb strength and areas the Lenz vector operator on an equivalent footing with different operators akin to classically conserved amounts. a few tricky to discover proofs and derivations are integrated as is improvement of operator formalism that allows facile answer of the Stark impression in hydrogen.
Discussion of the classical hydrogen atom can be provided. utilizing the correspondence precept this offers a transition from classical to quantum strategies. it's also tailored to describing yes features of multi-electron atoms.
The ebook is meant for graduate scholars who've had introductory quantum mechanics, yet undergraduates who've had this sort of direction may also make the most of it. There are greater than 80 difficulties on the ends of chapters with all solutions given. a close recommendations guide, on occasion giving a couple of resolution, is out there to instructors.
Charles E. Burkhardt earned his Ph.D. in experimental atomic physics at Washington college in St. Louis in 1985. he's Professor of Physics at Florissant Valley neighborhood collage in St. Louis. Jacob J. Leventhal earned his Ph.D. in experimental atomic physics on the college of Florida in 1965. he's Curators' Professor on the collage of Missouri вЂ“ St. Louis. they've got collaborated on experimental atomic physics on account that 1980, publishing a number of papers in study and educating journals.
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Consider a particle of mass µ subjected to a two-dimensional harmonic oscillator potential in which the force constants for the x- and y-components of motion are k x = k y = k. Show that the Schr¨odinger equation is separable in Cartesian coordinates. How many quantum numbers are there? Find an expression for the energy of this oscillator and discuss degeneracy. Do you think that the problem is separable in any other coordinate system? If so, which one? Why? 2. Consider a particle of mass µ conﬁned to a two-dimensional circular “box” of radius a such that V (ρ) = 0 ρ < a = ∞ otherwise Show that the Schr¨odinger equation is separable in polar coordinates ρ, φ.
A) Find the eigenvectors of the operator Sˆ y in terms of |α and |β , the eigenvectors of Sˆ z . Express them as spinors. (b) Suppose that an electron is in the spin state 1 √ 5 2 −1 with the Sˆ z eigenvectors as the basis. If we measure the y-component of the spin, what is the probability for ﬁnding a value of +(1/2)¯h ? 9. Use the spin 1 Sˆ z eigenstates as a basis to form the matrix representations of the angular momentum operators. 10. An unpolarized beam of neutral spin-1 particles is passed through a Stern– Gerlach device with magnetic ﬁeld in the y-direction, an SGy device.
75) vanishes unless j = j . 75) vanishes. 78) vanishes under the following The coefﬁcient of jm|V| circumstances. 1. 2. 3. 4. j j j j + = + − j j j j = −2. = 0. = 0. = ±1. The ﬁrst of these is impossible because j ≥ 0. The second is irrelevant because j = j is (temporarily) excluded. The third is excluded for the same reasons as the ﬁrst two. 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 .