nonlinear integral equationPerk-Schultz modelquantum Jacobi-Trudi and Giambelli formulaquantum transfer matrixthermodynamic Bethe ansatzT-systemWe analyze the perturbative series of the Keldysh-type sigma-model
It can be proved that the solutions of this equation system are curves contained in the hypersurfaces K = constant of the phase space x1 –x2 –x3 –t –k1 –k2 –k3 –ω—that is, the function K is a first integral of the system (Arnold, 1976). A function F(x1, x2, x3, t...
The Hamiltonian, like the Lagrangian, is a function that summarizes equations of motion. It has the additional interpretation of giving the total energy of a system. Though originally stated for classical mechanics, it is also an important part of quantum mechanics. Equations Start from the Lagrang...
[that is in fact the eq. (7)], the Maxwell-Ampère equation and the Schrödinger equation. However, in the hamiltonian formalism, at the semiclassical level as well as in the quantum theory, the Maxwell-Gauss equation is considered as a constraint that the solutions have to satisfy (see ...
A similar requirement must be placed on the denominator in Eq. 12 of Kutzelnigg (2007) for the equation to provide a secure definition. 5. This means that the permutation and its inverse are always in the same class. A group with this property is said to be anambivalentgroup. ...
Hamilton also calls this the “equation of the characteristic function” (Hamilton1834, 252). (Goldstine1980, 111); (Fraser2003, 361–363). (Hankins1980, 186). (Hankins1980, 183). This was a common assumption at the time. (Dürr and Teufel2009, 16). ...
The quantum Josephson Hamiltonian of two weakly linked Bose-Einsteincondensates is written in an overcomplete phase representation, thus avoidingthe problem of defining a Hermitian phase operator. We discuss the limit ofvalidity of the standard, non-rigorous Mathieu equation, due to the onset of a...
The light-atom state |ψ(t)〉 should satisfy the following time-dependent Schrodinger equation: i ∂ ∂t ψ(t; α) = HˆI ψ(t; α) , (5) wginihviteeirnaelbHliˆygI h|iψst-(aa0nt;oiαmn)t〉es r=taac t|etgi〉oi s⊗ng H|iαvae〉mn. Wiblt...
There is also a brief introduction to path integrals and their connection with Hamilton's principle, and the relation between the Hamilton-Jacobi equation of mechanics, the eikonal equation of optics, and the Schrodinger equation of quantum mechanics. 拉格朗日及汉密尔敦力学LAGRANGIAN AND HAMILTONIAN ...
THOMAS-BARGMANN-MICHEL-TELEGDI EQUATION FOR WIGNER PARTICLES INTRODUCTION The present contribution is an attempt towards a covariant Hamiltonian description for a quantum mechanical (as well as classical) system of elementary particles in interaction. (i) It is an attempt because the only problem which...