【導(dǎo)讀】本科畢業(yè)論文（設(shè)計(jì)）。題目范德瓦爾斯力的產(chǎn)生機(jī)理及其計(jì)算。專業(yè)班級(jí)09物理學(xué)01班。設(shè)計(jì)所在單位西安文理學(xué)院。本文從范德瓦爾斯力是分子間的弱的靜電相互作用出發(fā)，通過理論分析、構(gòu)建。究了這三種力的產(chǎn)生機(jī)理，得出了它們各自的計(jì)算式并以此得出了范德瓦爾斯力的。最后運(yùn)用宏觀響應(yīng)理論深入分析了低維度情況下色散力的計(jì)算。

　　

【正文】 q. (1) with G(S)(rA,rA,w), where G(S)(r,r39。,w) is the scattering part of the Green tensor. Hence, ? ? ? ?,AraAaa rUrUE ?? ? (2) ? ? ? ? ? ?? ? ? ????? b baAASabababAora dirrGddcrU 0 22 220 ,1 ??? ????? (3) ? ? ? ? ? ? ? ?? ????? b baabAASabababAra drrGdcrU ???? ,Re1 220 (4) where Ua(rA) has been deposed into an offresonant part U~f(rA) and a resonant part U~(rA), by taking into account the analytic properties of the Green tensor as a function of plex w, and considering explicitly the singularities excluded by the principalval ne integration in Eq. (1). Let us restrict our attention to groundstate at0111S. (Forces on excited atoms lead to dynamical problems in general [2]). In this case, there are of course no resonant contributions, as only upward transitions are possible [Wab 0 in Eq. (4)]. Thus, on identifying the (isotropic) groundstate polarizability of an atom as we may write the CP potential of a groundstate atom in the form of (see, . Refs. [16]) from which the force acting on the at0111 follows as 西安文理學(xué)院本科畢業(yè)設(shè)計(jì)（論文） 第 22 頁 ? ? ? ?AAF r U r? ?? (7) Now consider, instead of the force on a single groundstate atom, the force on a collection of groundstate at0111S distributed with a (coarsegrained) nUInber density 39。39。7(r) inside a space region of volume VriI. When the mutual interaction of the atoms can be disregarded, it is permissible to simply add up the CP forces on the individual atoms to obtain the force acting on the collection of atoms due to their interaction with the bodies outside the volume Vm, Le. Since the collection of atoms can be regarded as constituting a weakly dielectric body of susceptibility XNI(r, i~), Eq. (8) gives the Casimir force acting on such a body. Note that special cases of this formula were already used by Lifshitz [7] in the study of Casimir forces between dielectric plates. The question is how Eq. (8) can be generalized to an arbitrary groundstate body whose susceptibility XrvI (r,i~) is not necessarily small. An answer to this and related questions can be given by means of the Lorentzforce approach to dispersion forces, as developed in Refs. [8,9]. 2. Lorentz Force Let us consider macroscopic QED in a linearly, locally and causally responding medium with given (plex) permittivity c( r, w) and perrneability p( r, w). Then, if the current density that enters the macroscopic Maxwell equations is the sourcequantity representations of the electric and induction fields read as 西安文理學(xué)院本科畢業(yè)設(shè)計(jì)（論文） 第 23 頁 where the retarded Green tensor G(r,r39。,w) corresponds to the prescribed medium. In Eqs. (12) and (13), it is assumed that the medium covers the entire space so that solutions of the homogeneous Maxwell equations do not appear. Freespace regions can be introduced by performing the limits E ~ 1 and JL ~1, but not before the end of the actual calculations. Because of the polarization and/or magization currents attributed to the medium, the total charge and current densities are given by where As we have not yet specified the current density IN(r) in any way, the above formulas are generally valid so far, and they are valid both in classical and in quantum electrodynamics, In any case, it is clear that knowledge of the correlation function (IN(r,w)l~(r39。39。w39。)), where the angle brackets denote classical and/or quanturn averaging, is sufficient to C0111pute the correlation functions (e(r,w)Et(r39。,w39。)), (t(r,w),E(r39。,w39。)), (l(r,w)Bt(r39。,w39。)) and (t(r,w)B(r39。,w39。)), from which the (slowly varying part of the) Lorentz force density follows as Where the limit r39。~ r must be understood in such a way that divergent selfforces, 西安文理學(xué)院本科畢業(yè)設(shè)計(jì)（論文） 第 24 頁 which would be formally present even in a uniform (bulk) medium, are omitted. The force on the matter in a volurne Vf\,l is then given by the volume integral which can be rewritten as the surface integral where T(r) is (the expectation value of) Maxwell39。s stress tensor (as opposed to Minkowski39。s stress tensor), which is (formally) identical with the stress tensor in microscopic electrodynamics. Note that in going from Eq. (18) to Eq. (19), a term resulting from the (slowly varying part of the) Poynting vector has been omitted, which is valid under stationary conditions. If IN(r) can be regarded as being a classical current density producing classical radiation, IN(r) ~ jclass (r, t), then the Lorentz force puted in this way gives the classical radiation force that acts on the material inside the chosen space region of volume Vm (see also Ref. [10]). 3. Dispersion Force As already mentioned in Sec. 1, the dispersion force is obtained if IN(r) is identified with the noise current density attributed to the polarization and magization of the material. Let us restrict our attention to the zerotemperature limit, Le. let us assume that the overall system is in its ground state. (The generalization to thermal states is straightforward.) From macroscopic QED in dispersing and absorbing linear media [11,12] it can be shown that the relevant current correlation function reads as (I, unit tensor). Combining Eqs. (12), (13), (15), (16) and (20), and making use of standard properties of the Green tensor, one can then show that and 西安文理學(xué)院本科畢業(yè)設(shè)計(jì)（論文） 第 25 頁 Let us consider, for instance, an isolated dielectric body of volume Vl\rI and susceptibility XrvI(r,w) in the presence of arbitrary rnagodielectric bodies, which are well separated from the dielectric body. In this case, further evaluation of Eq. (18) leads to the following formula for the dispersion force on the dielectric body: where GrvI(r, r39。,i~) is the Green tensor of the system that includes the dielectric body. When the d