Quantum integrals of motion for variable quadratic Hamiltonians

被引：42

作者：

Cordero-Soto, Ricardo ^{[2
]}

Suazo, Erwin ^{[3
]}

Suslov, Sergei K. ^{[1
,2
]}

机构：

[1] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

[2] Arizona State Univ, Math Computat & Modeling Sci Ctr, Tempe, AZ 85287 USA

[3] Univ Puerto Rico, Dept Math Sci, Mayaguez, PR 00681 USA

来源：

ANNALS OF PHYSICS | 2010年 / 325卷 / 09期

基金：

美国国家科学基金会;

关键词：

The time dependent Schrodinger equation; Cauchy initial value problem; Green function; Propagator; Quantum damped oscillators; Caldirola-Kanai Hamiltonians; Quantum integrals of motion; Lewis-Riesenfeld dynamical invariant; Ermakov s equation; Ehrenfest s theorem; DEPENDENT HARMONIC-OSCILLATOR; NONLINEAR SCHRODINGER-EQUATIONS; COHERENT STATES; CHARGED-PARTICLE; WAVE-FUNCTIONS; ADIABATIC INVARIANTS; BERRY PHASE; SYSTEMS; QUANTIZATION; EVOLUTION;

D O I：

10.1016/j.aop.2010.02.020

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time dependent Schrodinger equation with variable quadratic Hamiltonians An extension of the Lewis-Riesenfeld dynamical invariant is given The time evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application (C) 2010 Elsevier Inc All rights reserved

引用

页码：1884 / 1912

页数：29

共 50 条

[41] Hall quantum Hamiltonians and electric 2D-curvature
Karasev, M. V.
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2012, 19 (03) : 299 - 306
[42] Spectra of Quantum KdV Hamiltonians, Langlands Duality, and Affine Opers
Frenkel, Edward
Hernandez, David
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2018, 362 (02) : 361 - 414
[43] How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics
Halpern, Nicole Yunger
Majidy, Shayan
NPJ QUANTUM INFORMATION, 2022, 8 (01)
[44] Quantum Simulations of Fermionic Hamiltonians with Efficient Encoding and Ansatz Schemes
Huang, Benchen
Sheng, Nan
Govoni, Marco
Galli, Giulia
JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 2023, 19 (05) : 1487 - 1498
[45] New Hamiltonians for loop quantum cosmology with arbitrary spin representations
Ben Achour, Jibril
Brahma, Suddhasattwa
Geiller, Marc
PHYSICAL REVIEW D, 2017, 95 (08)
[46] A Regularization of Quantum Field Hamiltonians with the Aid of p–adic Numbers
Sergio Albeverio
Andrew Khrennikov
Acta Applicandae Mathematica, 1998, 50 : 225 - 251
[47] Correct Quantum Chemistry in a Minimal Basis from Effective Hamiltonians
Watson, Thomas J., Jr.
Chan, Garnet Kin-Lic
JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 2016, 12 (02) : 512 - 522
[48] Quantum treatment of atom-field interaction via the quadratic invariant
Abdalla, M. Sebawe
Eleuch, H.
Perina, J.
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 2012, 29 (04) : 719 - 728
[49] Regarding Nonstationary Quadratic Quantum Systems
Sh. M. Nagiyev
A. I. Ahmadov
V. A. Tarverdiyeva
Sh. A. Amirova
Russian Physics Journal, 2019, 61 : 2173 - 2187
[50] Path integrals: From quantum mechanics to photonics
Robson, Charles W.
Tamashevich, Yaraslau
Rantala, Tapio T.
Ornigotti, Marco
APL PHOTONICS, 2021, 6 (07)

← 1 2 3 4 5 →