Related papers: The Jacobi principal function in Quantum Mechanics
It is shown that the parameters contained in any two complete solutions of the Hamilton-Jacobi equation, corresponding to a given Hamiltonian, are related by means of a time-independent canonical transformation and that, in some cases, a…
A function $\mathfrak{F}$ with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of $\mathfrak{F}$, first of all the Bessel functions of first…
Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…
The geometrical representation of the Jacobian in the path integral reduction problem which describes a motion of the scalar particle on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple Lie…
The direct integration of the harmonic oscillator path integral obscures the fundamental structure of its discrete, imaginary time propagator (density matrix). This work, by first proving an operator identity for contracting two free…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
The semi-classical approximation to black hole partition functions is not well-defined, because the classical action is unbounded and the first variation of the uncorrected action does not vanish for all variations preserving the boundary…
We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases…
A path integral evaluation of the Green's function for the hydrogen atom initiated by Duru and Kleinert is studied by recognizing it as a special case of the general treatment of the separable Hamiltonian of Liouville-type. The basic…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is…
Coherent state functional integral for the minisuperspace model of loop quantum cosmology is studied. By the well-established canonical theory, the transition amplitude in the path integral representation of loop quantum cosmology with…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
A brief excursion into the three-body problem in quantum mechanics is presented for graduate students or researchers in nuclear physics. Starting from single-particle coordinates, the three-body Schr\"{o}dinger equation is systematically…
We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
We discuss the Hamilton-Jacobi approach for a constrained system. We obtain the equation of motion for a singular system as total differential equations in many variables. We investigate the integrability conditions without using any gauge…