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Path integral formulation for eigenfunctions
Il Nuovo Cimento B Series 11, 1976We generalize the path integral technique of quantum mechanics to provide direct expressions for energy eigenfunctions. We illustrate our technique with the harmonic oscillator.
W. B. Campbell +3 more
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Berry’s phase through the path integral formulation
American Journal of Physics, 2007We study the evolution of a quantum system under adiabatic conditions using the path integral formulation. We obtain the Berry phase for systems with nondegenerate and degenerate energy spectra and recover well-known results. We also present a simple derivation of the adiabatic theorem.
Alves, M. A., Thomaz, M. T.
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Path-integral formulation of ion heating
The Physics of Fluids, 1988A description of the generation and evolution of ionospheric oxygen ion conic distributions by electromagnetic ion cyclotron resonance heating is formulated in terms of a path integral. All of the relevant physics is contained in this path integral, which may be used to calculate measurable properties of the conic distribution.
G. B. Crew, Tom Chang
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Path integral formulation of Roothaan's equations
International Journal of Quantum Chemistry, 1988AbstractThe generating functional Z(N) of the molecular orbital theory of N electrons has been projected into a subspace of atomic orbitals. By application of the saddle‐Point approximataions to the corresponding effective action, a set of equations of motion results. These equations are the classical Roothaan's equations of quantum chemistry.
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Path Integral Formulation for Chern-Simons Quantum Mechanics
International Journal of Theoretical Physics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Feng-Hua +3 more
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Integrating Gauge Fields in the ζ-Formulation of Feynman’s Path Integral
2020In recent work by the authors, a connection between Feynman's path integral and Fourier integral operator $ $-functions has been established as a means of regularizing the vacuum expectation values in quantum field theories. However, most explicit examples using this regularization technique to date, do not consider gauge fields in detail.
Hartung, Tobias, Jansen, Karl
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Path Integral Formulation of Quantum Electrodynamics
2016Let us consider a pure Abelian gauge theory given by the Lagrangian $$\displaystyle\begin{array}{rcl} \mathcal{L}_{\text{photon}}& =& -\frac{1} {4}F_{\mu \nu }F^{\mu \nu } \\ & =& -\frac{1} {4}\left (\partial _{\mu }A_{\nu } - \partial _{\nu }A_{\mu }\right )\left (\partial ^{\mu }A^{\nu } - \partial ^{\nu }A^{\mu }\right ){}\end{array}$$ (36.1)
Walter Dittrich, Martin Reuter
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