By Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe
Starting scholars of quantum mechanics usually event problems setting apart crucial underlying ideas from the categorical examples to which those ideas were traditionally utilized. Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this booklet to get rid of accurately those problems. Fourteen chapters supply a readability of association, cautious consciousness to pedagogical information, and a wealth of themes and examples which make this paintings a textbook in addition to a undying reference, permitting to tailor classes to fulfill scholars' particular wishes.
each one bankruptcy begins with a transparent exposition of the matter that's then handled, and logically develops the actual and mathematical proposal. those chapters emphasize the underlying ideas of the cloth, undiluted via broad references to purposes and useful examples that are positioned into complementary sections. The e-book starts off with a qualitative creation to quantum mechanical rules utilizing uncomplicated optical analogies and keeps with a scientific and thorough presentation of the mathematical instruments and postulates of quantum mechanics in addition to a dialogue in their actual content material. functions stick to, beginning with the easiest ones like e.g. the harmonic oscillator, and changing into progressively extra complex (the hydrogen atom, approximation equipment, etc.). The complementary sections every one extend this simple wisdom, providing quite a lot of purposes and comparable subject matters in addition to distinctive expositions of a big variety of distinct difficulties and extra complex themes, built-in as a necessary component of the text.
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Additional resources for Quantum Mechanics: Volume II
The second consists of the stationary states with well-defined angular momentum, that is, the eigenstates common to H , , L~ and L,, whose principal properties we pointed out in 43 C-2-b, c and d of chapter VIII. We intend to study here this second basis in more detail. In particular, we wish to derive a certain number of results used in chapter VIII. 1. The radial equation The Hamiltonian ( I ) commutes with the three components of the orbital angular momentum L of the particle: Consequently, we can apply the general theory developped in $ A of chaprer VII to this particular problem.
One of them is then the spherical Bessel function j,(p), which satisfies (50) and (55). For the other, we can choose the "spherical Neumann function of order 1", designated as n,(p), with the properties: 3. Relation b e t w e e n f r e e spherical w a v e s and plane w a v e s We alreadyknow two distinct bases of eigenstates of Ho: the plane waves u:O)(t) are eigenfunctions of the three components of the momentum P ; the free spherical waves cpLO),,(r) are eigenfunctions of L2 and L,. These two bases are different because P does not commute with L~ and L,.
If we take into account the linearity of Schrodinger's equation, we finally obtain (C-50). p. Explicit derivation Let us now consider formula (C-50), which was suggested by a physical approach to the problem, and let us show that it does indeed supply the desired expansion. First of all, the right-hand side of (C-50) is a superposition of eigenstates of H having the same energy t12k2/2p; consequently, this superposition remains a stationary state. Note that the expansion (C-31) brings in j,(kr)YP(B),that is, the free spherical wave cpP:,!
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