Solution of Some Differential Equations of Quantum Physics by the Numerical Functional Integration Method
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| 024 | 7 | 0 | |a 10.2478/cmam-2003-0035 |2 doi |
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| 245 | 0 | 0 | |a Solution of Some Differential Equations of Quantum Physics by the Numerical Functional Integration Method |h [Elektronische Daten] |
| 520 | 3 | |a The application of the numerical functional integration method to the solution of differential equations in quantum physics is discussed. We have developed a method of numerical evaluation of functional integrals in abstract complete separable metric spaces, which proves to have important advantages over the conventional Monte Carlo method of path integration. One of the considered applications is the investigation of open quantum systems (OQS), i.e., systems interacting with their environment. The density operator of OQS satisfies the known Lindblad differential equation. We have obtained the expression for matrix elements of this operator in the form of the double conditional Wiener integral and considered its application to some problems of nuclear physics. Another application is the solution of the Scr¨odinger equation with imaginary time and anticommuting variables for studying many-fermion systems. We have developed a numerical method based on functional integration over ordered subspaces. The binding energies of some nuclei are computed using this method. Comparison of the results with those obtained by other authors and with experimental values is presented. | |
| 540 | |a This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. | ||
| 690 | 7 | |a functional integral |2 nationallicence | |
| 690 | 7 | |a Wiener measure |2 nationallicence | |
| 690 | 7 | |a open quantum system |2 nationallicence | |
| 690 | 7 | |a density matrix |2 nationallicence | |
| 690 | 7 | |a propagator |2 nationallicence | |
| 690 | 7 | |a approximation formula |2 nationallicence | |
| 690 | 7 | |a fermion |2 nationallicence | |
| 690 | 7 | |a binding energy |2 nationallicence | |
| 690 | 7 | |a computations |2 nationallicence | |
| 700 | 1 | |a Lobanov |D Y. Y. |u Joint Institute for Nuclear Research, Laboratory of Information Technologies, 141980 Dubna, Moscow Region, Russia. | |
| 700 | 1 | |a Zhidkov |D E. P. |u Joint Institute for Nuclear Research, Laboratory of Information Technologies, 141980 Dubna, Moscow Region, Russia. | |
| 773 | 0 | |t Computational Methods in Applied Mathematics |d De Gruyter |g 3/4(2003), 560-578 |x 1609-4840 |q 3:4<560 |1 2003 |2 3 |o cmam | |
| 856 | 4 | 0 | |u https://doi.org/10.2478/cmam-2003-0035 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.2478/cmam-2003-0035 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Lobanov |D Y. Y. |u Joint Institute for Nuclear Research, Laboratory of Information Technologies, 141980 Dubna, Moscow Region, Russia | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zhidkov |D E. P. |u Joint Institute for Nuclear Research, Laboratory of Information Technologies, 141980 Dubna, Moscow Region, Russia | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Computational Methods in Applied Mathematics |d De Gruyter |g 3/4(2003), 560-578 |x 1609-4840 |q 3:4<560 |1 2003 |2 3 |o cmam | ||
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