相关论文: Quantum mechanics in general quantum systems (IV):…

Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of…

We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…

In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…

We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for non-Hermitian quantum systems. Initially we identify a point transformation as a…

In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum…

We consider the backreaction of a quantum system $q$ on an effectively classical degree of freedom $C$ that is interacting with it. The backreaction equation based on the standard path integral formalism gives the so-called `in-out'…

Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy.…

We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators.…

Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…

Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…

Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum…

This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…

It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…

We obtain a complete series solution of stationary Schr\"odinger's equation in the general quantum systems. It is exact in the sense that any approximation means is not used, or that the whole corrections or contributions from all order…

The generalized Weyl transform of index $\alpha$ is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation…

We extend a path-integral approach to bosonization previously developed in the framework of equilibrium Quantum Field Theories, to the case in which time-dependent interactions are taken into account. In particular we consider a non…

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…

We study the quantum evolution under the combined action of the exponentials of two not necessarily commuting operators. We consider the limit in which the two evolutions alternate at infinite frequency. This case appears in a plethora of…

While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…

In this paper we address the relation between the star exponentials emerging within the Deformation Quantization formalism and Feynman's path integrals associated with propagators in quantum dynamics. In order to obtain such a relation, we…