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1.
On the Schrödinger equation and the eigenvalue problem 总被引:1,自引:0,他引:1
If
k
is thek
th eigenvalue for the Dirichlet boundary problem on a bounded domain in
n
, H. Weyl's asymptotic formula asserts that
, hence
. We prove that for any domain and for all
. A simple proof for the upper bound of the number of eigenvalues less than or equal to - for the operator –V(x) defined on
n
(n3) in terms of
is also provided.Research partially supported by a Sloan Fellowship and NSF Grant No. 81-07911-A1 相似文献
2.
C. Quesne 《International Journal of Theoretical Physics》1999,38(7):1905-1923
GLh(n) ×GLh(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras
are built in terms of thecorresponding Rh and
-matrices by contracting theGLq(n) ×
-covariant q-bosonic (or q-fermionic) algebras
, = 1, 2.When using a basis of
wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n))
, a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of
(2, 1). 相似文献
3.
We derive explicit formulas for the multipoint series of
in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of
. We also obtain explicit formulas for the Hodge integrals
, in the cases i=0 and 1. 相似文献
4.
We show that there are canonical isomorphisms between Hochschild cohomology spaces
, where
is the algebra of smooth functions on a manifold M and
the space of skew multivector fields over M. This implies that continuous and differential deformation theories of
coincide. 相似文献
5.
Let an external current, whose support is confined to the space-like slab |x
0| < T in two-dimensional spacetime, build up a localized charge density which vanishes for times |x
0| > T. We show that the zero mass Dirac quantum field reacts to this current by a c-number shift of the fermion number, i.e. Q
out=Q
in+Q, with
, where q(x
0) denotes the total external charge. For the shift of the axial charge we obtain an extension of existing results. 相似文献
6.
C. Fronsdal 《Letters in Mathematical Physics》1991,22(3):225-228
The irreducible R-matrices associated with the quantum Liouville and sine-Gordon equations were classified by the su(2) index l, 2l integer. We find that the associated quantum field theories must have the following equal time operator product expansions in the lattice approximation
相似文献
7.
L. Burakovsky 《Foundations of Physics》1998,28(10):1595-1605
We show that linear Regge trajectories for mesons and glueballs, and the cubic mass spectrum associated with them, determine a relation between the masses of the meson and the scalar glueball,
, which implies
MeV. We also discuss relations between the masses of the scalar, tensor and 3-- glueballs,
, which imply
MeV. 相似文献
8.
J. Nowotny M. Rekas W. Weppner 《Applied Physics A: Materials Science & Processing》1988,47(2):205-208
Thermoelectric power (TP) and electrical conductivity (EC) measurements were performed for YEa2Cu3Ox at 1128 K under controlled oxygen partial pressure varying between 50 and 105 Pa. Three regimes are observed for the electrical properties. At low
both TP and EC remain constant with
. In the medium range
sharp changes of both electrical parameters occur; TP changes sign from positive above 4×102 Pa to negative below this
value. In the high
region (>7.6×103 Pa) TP vs log
exhibits two slopes; 5.1 below 1.5×104 Pa and 8.4 above this
value. The slopes can be discussed in terms of the defect structure involving singly and doubly ionized oxygen vacancies below and above 7.6×103 Pa, respectively. 相似文献
9.
We present empirical relations that connect the dimensionless ratios of low energy fermion masses for the charged lepton, up-type quark and down-type quark sectors and the CKM elements:
and
. Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases,
. According to this relation the measured value of
is close to the maximum value that can be reached,
for
. Finally, the particular mass relations between the quark and charged lepton sectors find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.Received: 31 July 2004, Revised: 22 September 2004, Published online: 9 November 2004 相似文献
10.
Hugo Parr 《Zeitschrift für Physik B Condensed Matter》1976,25(4):359-361
We have calculated analytically the superheating fieldH
sh
for bulk superconductors, correct to second order in. We find
, which agrees well with numerical computations for<0.5. The surface order parameter is
, and the penetration depth is
. 相似文献
11.
In the minimal supersymmetric standard model (MSSM), we study the light Higgs boson radiation off a light-chargino pair in the process
at linear colliders with
GeV. We analyze cross sections in the regions of the MSSM parameter space where the process
cannot proceed via on-shell production and subsequent decay of either heavier charginos or the pseudoscalar Higgs boson A. Cross sections up to a few fb are allowed, according to present experimental limits on the Higgs boson, chargino and sneutrino masses. We also show how a measurement of the
production rate could provide a determination of the Higgs boson couplings to charginos.Received: 24 June 2004, Revised: 13 May 2005, Published online: 19 July 2005 相似文献
12.
We give a complete characterization, including a Lévy–Itô decomposition, of Poincaré-invariant Markov processes on
, the relativistic phase space in 1+1 spacetime dimensions. Then, by means of such processes, we construct Poincaré-invariant Gaussian random fields, and we prove a no-go theorem for the random fields corresponding to Brownian motions on
. 相似文献
13.
We prove that Gibbs states for the Hamiltonian
, with thes
x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if
withJ
xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions. 相似文献
14.
On the basis of the S-matrix approach, a theory of perturbations in 1/Z is developed; the energy of a multielectron system is written in the form of a double series in powers of andZ and a method of determining the coefficients of this series in a j-j coupling scheme is given. The method is applied to configurations of the type
, and numerical results are given for the wavelength of transitions between several states of the isoelectronic as sequence of carbon, illustrating the good agreement between experiment and theory.Translated from Izvestiya Vysshikh Uchebnikh Zavedenii, Fizika, No. 8, pp. 59–63, August, 1978. 相似文献
15.
It is shown that in a quantum field theory describing free, scalar particles with masses m
i
, i there exist locally normal equilibrium states with finite energy density for all temperature >0 if and only if
. This result lends support to the conjecture that the nuclearity criterion proposed by Buchholz and Wichmann is sensitive to the thermodynamical properties of field-theoretic models. 相似文献
16.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
17.
A. Werthmüller A. Adamczak R. Jacot‐Guillarmod F. Mulhauser L.A. Schaller L. Schellenberg H. Schneuwly Y.‐A. Thalmann S. Tresch 《Hyperfine Interactions》1998,116(1-4):1-16
The charge exchange reaction of negative muons from the
atom to oxygen has been measured in gaseous mixtures of H2 + O2. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of
, describing the transfer from the ground state of thermalized
atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the
thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate
=3.9
1011 s-1 in the energy interval 0.12–0.22 eV. The analysis with the model of Two components shows that all measured time spectra can be reproduced with the same set of parameters. 相似文献
18.
Stan Gudder 《Foundations of Physics》1999,29(6):877-897
This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events)
and the set of probability measures
on a measurable space
. An observable
is defined, where
is the value space of X. It is noted that there exists a one-to-one correspondence between states on
and elements of
and between observables
and -morphisms from
to
. Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map
is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived. 相似文献
19.
Bertfried Fauser 《International Journal of Theoretical Physics》2001,40(1):399-412
Daviau showed the equivalence of matrix Dirac theory, formulated within a spinor bundle
, to a Clifford algebraic formulation within space Clifford algebra
Pauli algebra (matrices) biquaternions. We will show, that Daviau's map :
is an isomorphism. It is shown that Hestenes' and Parra's formulations are equivalent to Daviau's Clifford algebra formulation, which uses outer automorphisms. The connection between different formulations is quite remarkable, since it connects the left and right action on the Pauli algebra itself viewed as a bi-module with the left (resp. right) action of the enveloping algebra
. The isomorphism established in this article and given by Daviau's map does clearly show that right and left actions are of similar type. This should be compared with attempts of Hestenes, Daviau, and others to interprete the right action as the iso-spin freedom. 相似文献
20.
Jouko Mickelsson 《Letters in Mathematical Physics》1991,22(2):131-139
An extension
of the symmetry group GL of Sato's universal Grassmannian GM is constructed. The extension plays a similar role to that of the central extension
in the approach of Segal and Wilson to functions and KP hierarchy. Our group G contains GLres as a subgroup and the associated function is a deformation of the usual function, leading to a deformed KP hierarchy. A relation to current algebra of Yang-Mills theory in 3+1 dimension is discussed. 相似文献
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