Self-stochasticity in boundary value problems of quantum mechanics
On the example of an initial-value boundary problem for the Schrödinger equation, a methodological problem of quantum mechanics has been discussed. It is shown that quantum mechanical problems can be reduced to difference equations with continuous time for which there exist so-called self-stochastic...
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| Datum: | 2017 |
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| Sprache: | English |
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України
2017
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| Schriftenreihe: | Физика и техника высоких давлений |
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| Zitieren: | Self-stochasticity in boundary value problems of quantum mechanics / I.B. Krasnyuk, T.N. Melnik, V.M. Yurchenko // Физика и техника высоких давлений. — 2017. — Т. 27, № 2. — С. 51-61. — Бібліогр.: 18 назв. — англ. |
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irk-123456789-1681382020-04-23T01:25:53Z Self-stochasticity in boundary value problems of quantum mechanics Krasnyuk, I.B. Melnik, T.N. Yurchenko, V.M. On the example of an initial-value boundary problem for the Schrödinger equation, a methodological problem of quantum mechanics has been discussed. It is shown that quantum mechanical problems can be reduced to difference equations with continuous time for which there exist so-called self-stochastic solutions. Hence, such solutions exist for quantum problems. These solutions are random function as time is large. It is shown that the Sharkovsky metric can be applied for computer simulation of limit distributions of random wave functions. Обсуждается методологическая проблема квантовой механики на примере краевой задачи с начальными условиями для уравнения Шредингера. Показано, что квантовомеханические задачи могут быть сведены к разностным уравнениям с непрерывным временем, для которых существуют так называемые самостохастические решения. Следовательно, такие решения существуют и для квантовых задач. На больших временах эти решения являются случайными функциями. Показано, что метрика Шарковского может быть применена для компьютерного моделирования предельных распределений случайных волновых функций. 2017 Article Self-stochasticity in boundary value problems of quantum mechanics / I.B. Krasnyuk, T.N. Melnik, V.M. Yurchenko // Физика и техника высоких давлений. — 2017. — Т. 27, № 2. — С. 51-61. — Бібліогр.: 18 назв. — англ. 0868-5924 PACS: 03.65.–w, 02.30.Jr http://dspace.nbuv.gov.ua/handle/123456789/168138 en Физика и техника высоких давлений Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
On the example of an initial-value boundary problem for the Schrödinger equation, a methodological problem of quantum mechanics has been discussed. It is shown that quantum mechanical problems can be reduced to difference equations with continuous time for which there exist so-called self-stochastic solutions. Hence, such solutions exist for quantum problems. These solutions are random function as time is large. It is shown that the Sharkovsky metric can be applied for computer simulation of limit distributions of random wave functions. |
| format |
Article |
| author |
Krasnyuk, I.B. Melnik, T.N. Yurchenko, V.M. |
| spellingShingle |
Krasnyuk, I.B. Melnik, T.N. Yurchenko, V.M. Self-stochasticity in boundary value problems of quantum mechanics Физика и техника высоких давлений |
| author_facet |
Krasnyuk, I.B. Melnik, T.N. Yurchenko, V.M. |
| author_sort |
Krasnyuk, I.B. |
| title |
Self-stochasticity in boundary value problems of quantum mechanics |
| title_short |
Self-stochasticity in boundary value problems of quantum mechanics |
| title_full |
Self-stochasticity in boundary value problems of quantum mechanics |
| title_fullStr |
Self-stochasticity in boundary value problems of quantum mechanics |
| title_full_unstemmed |
Self-stochasticity in boundary value problems of quantum mechanics |
| title_sort |
self-stochasticity in boundary value problems of quantum mechanics |
| publisher |
Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/168138 |
| citation_txt |
Self-stochasticity in boundary value problems of quantum mechanics / I.B. Krasnyuk, T.N. Melnik, V.M. Yurchenko // Физика и техника высоких давлений. — 2017. — Т. 27, № 2. — С. 51-61. — Бібліогр.: 18 назв. — англ. |
| series |
Физика и техника высоких давлений |
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AT krasnyukib selfstochasticityinboundaryvalueproblemsofquantummechanics AT melniktn selfstochasticityinboundaryvalueproblemsofquantummechanics AT yurchenkovm selfstochasticityinboundaryvalueproblemsofquantummechanics |
| first_indexed |
2025-07-15T02:40:21Z |
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2025-07-15T02:40:21Z |
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