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Path Integrals in Noncommutative Quantum Mechanics [PDF]
Theoretical and Mathematical Physics, 2003 Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.
Dragovich, Branko, Rakic, Zoran
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Quantum Oscillator at Temperature T and the Evolution of a Charged-Particle State in the Electric Field in the Probability Representation of Quantum Mechanics [PDF]
Entropy, 2023 A short review constructing the probability representation of quantum mechanics is given, and examples of the probability distributions describing the states of quantum oscillator at temperature T and the evolution of quantum states of a charged particle
Margarita A. Man’ko +1 more
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A new method for the calculation of functional and path integrals [PDF]
Scientific Reports, 2023 This paper addresses a disconnect between the pivotal role of functional (path) integrals in modern theories, such as quantum mechanics and statistical thermodynamics, and the currently limited ability to perform the actual calculation.
Amos A. Hari, Sefi Givli
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Closed Path Integrals and Renormalisation in Quantum Mechanics
, 2000 We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the $V \sim x^{4}$ potential. The renormalized action is relevant for
F. Cametti +18 more
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Introduction to path-integral Quantum Field Theory – A toolbox
Revista Brasileira de Ensino de Física, 2021 Lecture notes on path-integrals, suitable for an undergraduate course with prerequisites such as: Classical Mechanics, Electromagnetism and Quantum Mechanics.
Roland Koberle
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PATH INTEGRATION IN RELATIVISTIC QUANTUM MECHANICS [PDF]
International Journal of Modern Physics A, 1993 The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time.
Redmount, Ian H., Suen, Wai-Mo
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Renormalized path integral in quantum mechanics [PDF]
Journal of Mathematical Physics, 1997 We obtain direct, finite, formulations of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description requires a modification to the Wiener measure on continuous paths that describes an unusual diffusion process ...
Henderson, R. J., Rajeev, S. G.
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Differentiable-path integrals in quantum mechanics [PDF]
International Journal of Geometric Methods in Modern Physics, 2015 A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of Cα, by only allowing paths which possess at least α derivatives. The method introduces two external parameters, and induces the appearance of a particular time scale ϵD such that for time intervals longer than ϵD the model behaves ...
Koch, Benjamin, Reyes, Ignacio
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Path integrals: From quantum mechanics to photonics
APL Photonics, 2021 The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its dynamical evolution,
Charles W. Robson +3 more
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Natural space of the micro-object
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2011 The immutability of classical dynamical laws for the microscopic object in the space which coordinate axes are the transition matrix elements of the corresponding coordinates is proved. It is stated that measurement is a micro-object localization process
Aleksey Yu Samarin
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