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71.
谐振子薛定谔方程的简单解法 总被引:2,自引:0,他引:2
物质的许多物理与化学性质都可以用线性谐振子模型解释,本文用简单的数学运算求解线性谐振子的薛定谔方程,避免了特殊函数等复杂的数学运算,得出了量子力学教材完全相同的结果。 相似文献
72.
Tatsien Li 《Mathematical Methods in the Applied Sciences》2006,29(13):1543-1553
By means of a direct and constructive method based on the theory of semi‐global C2 solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
73.
Manfred Sommer 《Constructive Approximation》2006,23(2):211-227
Hermite interpolation of 2n + k data by spline spaces of order k with n variable knots counting multiplicities is studied.
A characterization of the minimal spline spaces which admit a solution of the interpolation problem is obtained. A sufficient
condition on uniqueness of interpolating spline functions is given. 相似文献
74.
Roderich Tumulka 《Foundations of Physics》2007,37(2):186-197
In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber
(RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type
theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys.
115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.
相似文献
75.
We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam,
which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive
relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and
focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has
been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are
elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius
of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed
to convert a circular Gaussian beam into an elliptic Gaussian beam. 相似文献
76.
A new approach to identify the independent amplitudes along with their partial wave multipole expansions, for photo-and electro-production
is suggested, which is generally applicable to mesons with arbitrary spin-parity. These amplitudes facilitate direct identification
of different resonance contributions.
相似文献
77.
In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions. 相似文献
78.
Robert J. Rubin 《Journal of statistical physics》1991,65(5-6):1207-1216
A one-dimensional lattice random walk in the presence ofm equally spaced traps is considered. The step length distribution is a symmetric exponential. An explicit analytic expression is obtained for the probability that the random walk will be trapped at thejth trapping site. 相似文献
79.
In this paper, we establish two general theorems for equivalence between the Meir–Keeler type contractive conditions and the contractive definitions involving gauge functions. One of these theorems is an extension of a recent result of Lim (On characterization of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120). 相似文献
80.
Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union
of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of
verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated
systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which
can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key
roles in solving large scale knowledge-based data classification problems where they are used to describe the containments
as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which
was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments. 相似文献