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The exact solution for the generalized time-dependent harmonic oscillator and its adiabatic limit
ANNALS
OF PHYSICS
203, 229-230
Abstracts
(1990)
of Papers
to Appear
in Future
Issues
Fluctuation in the de Sitter Universe. N. BANERJEE. Saha Institute of Nuclear Physics, 92 A.P.C. Road, Calcutta-700009, India; AND S. MALLIK. Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland.
Density
A scalar Higgs field theory in de Sitter space-time has been investigated using the real time formulation of Semenoff and Weiss. We calculate the two-point function at late times and use it to obtain a general expression for the amplitude of fluctuation in energy density on scales which come out of the de Sitter horizon.
The Exact
Solution
for
the Generalized
XIAO-CHUN GAO, JING-BO Xu, Hangzhou, China.
AND
Time-Dependent
Harmonic
Oscillator
and Its Adiabatic
Limit.
TIE-ZHENG QIAN. Department of Physics, Zhejiang University,
In this paper, we find the exact solution for the generalized time-dependent harmonic oscillator by making use of the Lewis-Riesenfeld theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry’s phase for the oscillator obtained. We proceed to use the exact solution to construct the coherent state and calculate the corresponding classical Hannay’s angle.
Quanrum
D#iiactive
Reflection
by a Periodic
Non-penetrable
Surface:
A Multiple
Scattering
Approach.
R. F. ALVAREZ-ESTRADA. Departamento de Fisica Teorica I, Facultad de Ciencias Fisicas, e Instituto de Fisica Fundamental, Universidad Complutense, 28040 Madrid, Spain. The diffractive reflection of a particle (an atom) by a periodically undulating, non-penetrable, and smooth surface S in three spatial dimensions is studied in detail. The determination of the particle wave function cp is reduced to that of a certain double-layer density, p. In turn, p is shown to fulfill an inhomogeneous linear integral equation of second kind, which can be solved by successive iterations. The convergence of the resulting series for p and q is established if S is suitably smooth. The known limit of reflection by a planar surface is recovered consistently. The case in which new reflected waves are created is studied. Approximate solutions are obtained when the de Broglie wavelength is much smaller than the periods of the surface. The reflection and diffraction in two spatial dimensions is outlined. The technique used in the present work can be regarded as non-trivial extensions to infinite periodic surfaces of the multiple reflection approach for Green’s functions inside hnite surfaces studied by Balian and Bloch.
of Yang-Mills Fields in a General Class of Linear Gauges. A. BURNEL. Physics Department, University of Liege, B-4000 Liege 1, Belgium; R. KOBES AND G. KUNSTATTER. Physics Department, University of Winnipeg, Winnipeg, Manitoba, Canada R3B 2E9; AND K. MAK. Physics Department, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
Quantization
A framework for the quantization of Yang-Mills fields in a general class of linear gauges is presented. This class contains most of the commonly used gauges, both covariant and non-covariant, and includes singular cases such as the Coulomb or timelike axial gauge as appropriate limits of the gauge
229 0003-4916/90
$7.50
Copyright 0 1990 by Academic Press, Inc. All rights of reproductmn m any form reserved
OF PHYSICS
203, 229-230
Abstracts
(1990)
of Papers
to Appear
in Future
Issues
Fluctuation in the de Sitter Universe. N. BANERJEE. Saha Institute of Nuclear Physics, 92 A.P.C. Road, Calcutta-700009, India; AND S. MALLIK. Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland.
Density
A scalar Higgs field theory in de Sitter space-time has been investigated using the real time formulation of Semenoff and Weiss. We calculate the two-point function at late times and use it to obtain a general expression for the amplitude of fluctuation in energy density on scales which come out of the de Sitter horizon.
The Exact
Solution
for
the Generalized
XIAO-CHUN GAO, JING-BO Xu, Hangzhou, China.
AND
Time-Dependent
Harmonic
Oscillator
and Its Adiabatic
Limit.
TIE-ZHENG QIAN. Department of Physics, Zhejiang University,
In this paper, we find the exact solution for the generalized time-dependent harmonic oscillator by making use of the Lewis-Riesenfeld theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry’s phase for the oscillator obtained. We proceed to use the exact solution to construct the coherent state and calculate the corresponding classical Hannay’s angle.
Quanrum
D#iiactive
Reflection
by a Periodic
Non-penetrable
Surface:
A Multiple
Scattering
Approach.
R. F. ALVAREZ-ESTRADA. Departamento de Fisica Teorica I, Facultad de Ciencias Fisicas, e Instituto de Fisica Fundamental, Universidad Complutense, 28040 Madrid, Spain. The diffractive reflection of a particle (an atom) by a periodically undulating, non-penetrable, and smooth surface S in three spatial dimensions is studied in detail. The determination of the particle wave function cp is reduced to that of a certain double-layer density, p. In turn, p is shown to fulfill an inhomogeneous linear integral equation of second kind, which can be solved by successive iterations. The convergence of the resulting series for p and q is established if S is suitably smooth. The known limit of reflection by a planar surface is recovered consistently. The case in which new reflected waves are created is studied. Approximate solutions are obtained when the de Broglie wavelength is much smaller than the periods of the surface. The reflection and diffraction in two spatial dimensions is outlined. The technique used in the present work can be regarded as non-trivial extensions to infinite periodic surfaces of the multiple reflection approach for Green’s functions inside hnite surfaces studied by Balian and Bloch.
of Yang-Mills Fields in a General Class of Linear Gauges. A. BURNEL. Physics Department, University of Liege, B-4000 Liege 1, Belgium; R. KOBES AND G. KUNSTATTER. Physics Department, University of Winnipeg, Winnipeg, Manitoba, Canada R3B 2E9; AND K. MAK. Physics Department, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
Quantization
A framework for the quantization of Yang-Mills fields in a general class of linear gauges is presented. This class contains most of the commonly used gauges, both covariant and non-covariant, and includes singular cases such as the Coulomb or timelike axial gauge as appropriate limits of the gauge
229 0003-4916/90
$7.50
Copyright 0 1990 by Academic Press, Inc. All rights of reproductmn m any form reserved