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 authors propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schrodinger equation using point canonical transformation method and obtain ground state eigenfunction.
Abstract: In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schrodinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position dependent mass Schrodinger equation. We fix the ladder operators in the deformed form and obtain explicit expression of the deformed superpotential in terms of mass distribution and its derivative. We also prove that these deformed operators lead to minimum uncertainty relations. Further, we illustrate our algorithm with two examples, in which the coherent states given for the second example are new.
39 citations
TL;DR: In this paper, it is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass and the time-dependent first integrals of motion are obtained from the factorization of such a constant.
Abstract: We analyze the dynamical equations obeyed by a classical system with position- dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the Hamiltonian for this system and find the modifications required in the Euler{Lagrange and Hamilton's equations to reproduce the appropriate Newton's dynamical law. Since the Hamiltonian is not time invariant, we get a constant of motion suited to write the dynamical equations in the form of the Hamilton's ones. The time-dependent first integrals of motion are then obtained from the factorization of such a constant. A canonical transformation is found to map the variable mass equations to those of a constant mass. As particular cases, we recover some recent results for which the dependence of the mass on the position was already unnoticed, and find new solvable potentials of the Poschl{Teller form which seem to be new. The latter are associated to either the su(1;1) or the su(2) Lie algebras depending on the sign of the Hamiltonian.
39 citations
TL;DR: In this article, an effective Hamiltonian for the quasiparticles was derived using a canonical transformation approach, which takes into account the effect of hole interactions with the short-range spin waves and to describe the single-hole ground state.
Abstract: The t-J model in the spinless-fermion representation is studied. An effective Hamiltonian for the quasiparticles is derived using a canonical transformation approach. It is shown that the rather simple form of the transformation generator allows one to take into account the effect of hole interactions with the short-range spin waves and to describe the single-hole ground state. Obtained results are very close to ones of the self-consistent Born approximation. Further accounting of the long-range spin-wave interaction is possible on a perturbative basis. Spin-wave exchange and an effective interaction due to minimization of the number of broken antiferromagnetic bonds are included in the effective quasiparticle Hamiltonian. The two-hole bound state problem is solved using a Bethe-Salpeter equation. The only bound state found to exist in the region of 1{lt}(t/J){lt}5 is the d wave. Both types of the hole-hole interaction are important for its formation. A discussion of the possible relation of the obtained results to the problem of superconductivity in real systems is presented. {copyright} {ital 1997} {ital The American Physical Society}
39 citations
TL;DR: In this article, it was shown that S-duality in four dimensional non-supersymmetric abelian gauge theories can be formulated as a canonical transformation in the phase space of the theory.
39 citations
TL;DR: In this article, the authors studied first and second-order intertwining approaches to generate isospectral partner potentials of position dependent (effective) mass Schrodinger equation.
Abstract: Here, we have studied first- and second-order intertwining approaches to generate isospectral partner potentials of position dependent (effective) mass Schrodinger equation. The second-order intertwiner is constructed directly by taking it as second-order linear differential operator with position dependent coefficients, and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained, which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to remove bound state(s), and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. ...
39 citations