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1.
FAN Hong-Yi FAN Yue 《理论物理通讯》2005,44(2):252-254
We extend the method of searching “eigen-operator” of the square of the Schroedinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also leads to a new uncertainty relation regarding to the free Hamiltonian and the interacting Hamiltonian. 相似文献
2.
Oleg Lisovyy 《Letters in Mathematical Physics》2006,77(1):63-81
We introduce and study a family of quantum fields, associated to δ-interactions in one dimension. These fields are analogous to holonomic quantum fields of Sato et al. in Holonomic quantum fields I–V (Publ. RIMS, Kyoto University, 14: 223–267, 1978; 15: 201–278, 1979; 15: 577–629, 1979; 15: 871-972, 1979; 16: 531–584, 1979). Corresponding field operators belong to an infinite-dimensional representation of the group
in the Fock space of ordinary harmonic oscillator. We compute form factors of such fields and their correlation functions, which are related to the determinants of Schroedinger operators with a finite number of point interactions. It is also shown that these determinants coincide with tau functions, obtained through the trivialization of the det*-bundle over a Grassmannian associated to a family of Schroedinger operators. 相似文献
3.
SHEN Shou-Feng ZHANG Jun YE Cai-Er PAN Zu-Liang 《理论物理通讯》2005,44(4):604-608
In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger (NLS) system are obtained directly. When the modulus m → 1, those periodic solutions degenerate as the corresponding envelope soliton solutions, envelope shock wave solutions. Especially, for the 3-coupled NLS system, five types of Jacobi elliptic function envelope solutions are illustrated both analytically and graphically. Two types of those degenerate as envelope soliton solutions. 相似文献
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利用Weierstrass椭圆函数展开法对非线性光学、等离子体物理等许多系统中出现的立方非线性 Schr(o)dinger方程进行了研究.首先通过行波变换将方程化为一个常微分方程,再利用Weierstrass椭圆函数展开法思想将其化为一组超定代数方程组,通过解超定方程组,求得了含Weierstrass椭圆函数的周期解,以及对应的Jacobi椭圆函数解和极限情况下退化的孤波解.该方法有以下两个特点:一是可以借助数学软件Mathematica自动地完成;二是可以用于求解其它的非线性演化方程(方程组). 相似文献
6.
讨论光通信中脉冲的准单色光光场的正负频表示,正负频形式的傅里叶变换,正负频形式的非线性薛定谔方程及它们之间的关系.尤其在脉冲频谱的求解问题中,如果采用负频形式的非线性薛定谔方程则必须选取负频形式的傅里叶变换;如果采用正频形式的非线性薛定谔方程则必须选取正频形式的傅里叶变换.采用分步傅里叶法对具体实例进行数值求解,验证了讨论结果. 相似文献
7.
We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger (NLS) equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations. 相似文献
8.
CHEN Gang XUAN Pei-Cai CHEN Zi-Dong 《理论物理通讯》2006,46(1):39-42
In this paper, two novel semiclassical methods including the standard and supersymmetric WKB quantization conditions are suggested to discuss the Schroedinger equation with position-dependent effective mass. From a proper coordinate transformation, the formalism of the Schroedinger equation with position-dependent effective mass is mapped into isospectral one with constant mass and therefore for a given mass distribution and physical potential function the bound state energy spectrum can be determined easily by above method associated with a simple integral formula. It is shown that our method can give the analytical results for some exactly-solvable quantum systems. 相似文献
9.
V. Majerník 《Foundations of Physics Letters》1997,10(4):357-370
We propose a spacetime scheme representing the union of the real and non-real spacetime as a possible geometrical framework
for Caldirola’s idea, that the bradyonic motion can be regarded as a light-like motion in an additional extra space. The playground
of all physical processes is the union space. However, the physical processes in union space are differently projected on
the real and non-real spacetime. The waves linked with luxons in union space are projected on the real spacetime so that they
propagate here always with the velocity of light. The waves linked with bradyons in union space are projected on the non-real
spacetime so that they propagate here with the velocity of light. The wave linked with a bradyon in union space, which is
projected on the real spacetime, is here described by the Schroedinger and Dirac equations. There is proposed a symmetry which
demands that the physical world is in its law the same whether it is seen from real or non-real spacetime. We discuss some
consequences of this symmetry in the theory of elementary particles. 相似文献
10.
本文讨论了一类带调和势|x|^2的非线性Schroedinger方程解的长时间行为,证明了整体吸引子的存在性. 相似文献