Topic
Canonical transformation
About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the boundedness of all the solutions for the 2π-periodic equation x + ax+−bx− = f(t) is considered. But the bounded solutions are not bounded in the sense that a and b are positive constants.
Abstract: In this paper we consider the boundedness of all the solutions for the equation x″ + ax+−bx− = f(t) is a smooth 2π-periodic function, a and b are positive constants (a≠b).
7 citations
TL;DR: In this paper, the strong coupling method in meson field theory is described and a general scheme for a strong coupling approximation method based on this field splitting is derived, and the problem of calculating the pion-nucleon resonance scattering from strong coupling theory is treated on this basis.
7 citations
TL;DR: In this paper, the free electromagnetic field is canonically quantized in a gauge-invariant way by interpreting the Fourier coefficients of the magnetic induction field B as generalised coordinates, and the coefficient of the electric field E as their conjugate momenta.
Abstract: The free electromagnetic field is canonically quantised in a gauge-invariant way by interpreting the Fourier coefficients of the magnetic induction field B as generalised coordinates, and the coefficients of the electric field E as their conjugate momenta. The usual commutation relations among the components of E and B are obtained. A canonical transformation, corresponding to a rotation in generalised phase space, is made on the Fourier coefficients. This transformation is shown to give a duality transformation on the electric and magnetic fields. The free-field Maxwell equations and the commutation relations are invariant under duality transformations. However, if interactions are introduced, the invariance under duality transformations is broken, and the original canonical theory should be used.
7 citations
TL;DR: In this paper, a modification of a generalized translation operator was proposed by including a $q$exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator and its canonically conjugate deformed position operator.
Abstract: We propose a modification of a recently introduced generalized translation operator, by including a $q$-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator $\hat{p}_q$, and its canonically conjugate deformed position operator $\hat{x}_q$. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual $q$-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
7 citations
Abstract: We consider the interaction between a two-level atom and a quantum system that consists of three electromagnetic fields. An analytic solution is provided for the wave function of a pairwise mutual interaction between a two-level atom and three modes using a frequency converter. SU(2) group generators are used to describe these field mode interactions. In addition, a canonical transformation is employed in order to convert the Hamiltonian model into a Jaynes–Cumming-like model, which is used to solve the Schrodinger equation. Statistical properties related to the atomic inversion, entanglement, and squeezing phenomena are discussed. Superstructure patterns and partial disentanglement, as well as squeezing swapping between quadratures, are displayed for selected parameters.
7 citations