Journal ArticleDOI
Quantum Mechanical Path Integrals With Wiener Measures for All Polynomial Hamiltonians
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In this paper, the authors constructed arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well defined path integrals involving Wiener measure on phase space.Abstract:
We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well defined path integrals involving Wiener measure on phase space, as the diffusion constant diverges. A related construction achieves a similar result for an arbitrary spin Hamiltonian.read more
Citations
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Analytic representations in quantum mechanics
TL;DR: In this article, various Euclidean, hyperbolic and elliptic analytic representations of the harmonic oscillator are discussed and relations among them are discussed, and the general theory that relates the growth of analytic functions with the density of their zeros is applied to Bargmann functions and leads to theorems on the completeness of sequences of Glauber coherent states.
Journal ArticleDOI
A numerical evaluation of the semiclassical coherent state path integral
TL;DR: In this article, the authors evaluated the coherent state path integral developed by Klauder for a chaotic system (the kicked rotator) and found that it provides an accurate time evolution of a wave function over a finite time period even for the chaotic system.
Journal ArticleDOI
Effect of time-dependent basis functions and their superposition error on atom-centered density matrix propagation (ADMP): connections to wavelet theory of multiresolution analysis.
TL;DR: Computational study of the weakly bound water dimer illustrates that basis set superposition error is much less for basis functions beyond the 6-31+G(*) level of Gaussians when structure, energetics, frequencies, and radial distribution functions are to be calculated.
Journal ArticleDOI
Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems.
TL;DR: A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented and one notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately.
Journal ArticleDOI
Quasiclassical path integral in coherent-state manifolds
TL;DR: In this article, the authors considered quantization of classical dynamical systems with a Poisson structure on homogeneous Kahler manifolds and represented the unitary transition operator as a quasiclassical path integral in the coherent-state basis.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Journal ArticleDOI
Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability
Lucien Le Cam,Neyman Jerzy +1 more
Book
Techniques and Applications of Path Integration
TL;DR: In this paper, the authors present a list of applications of the path integral formula in statistical mechanics, including the application of the Path Integral formula to Statistical Mechanics, asymptotic analysis, and the phase space path integral.
Book
Special Functions and the Theory of Group Representations
TL;DR: In this paper, a standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special function are related to (and derived from) simple well-known facts of representation theory.