Related papers: Quantum Hamilton-Jacobi Theory
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
We study the homogenization of first-order Hamilton-Jacobi equations on an infinite-dimensional Hilbert space, motivated by systems of infinitely many indistinguishable particles on the torus. A central difficulty is that the analysis takes…
The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor)…
Beyond their use as numerical tools, quantum trajectories can be ascribed a degree of reality in terms of quantum measurement theory. In fact, they arise naturally from considering continuous observation of a damped quantum system. A…
Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in…
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms…
Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical…
In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also…
We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation.…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…
For one dimensional motions, we derive from the Dirac Spinors Equation (DSE) the Quantum Stationary Hamilton-Jacobi Equation for particles with spin 1/2. Then, We give its solution. We demonstrate that the $QSHJES_{1\over2}$ have two…
As a continuation of Rabei et al. work [11], the Hamilton- Jacobi partial differential equation is generalized to be applicable for systems containing fractional derivatives. The Hamilton- Jacobi function in configuration space is obtained…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\"odinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which…
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact…