{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T21:41:54Z","timestamp":1725745314266},"publisher-location":"Cham","reference-count":33,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319022963"},{"type":"electronic","value":"9783319022970"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-319-02297-0_30","type":"book-chapter","created":{"date-parts":[[2013,8,14]],"date-time":"2013-08-14T11:37:38Z","timestamp":1376480258000},"page":"369-380","source":"Crossref","is-referenced-by-count":2,"title":["A Quantum Measurements Model of Hydrogen-Like Atoms in Maple"],"prefix":"10.1007","author":[{"given":"L.","family":"Sevastianov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Zorin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Gorbachev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"30_CR1","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1103\/PhysRevLett.52.1064","volume":"52","author":"K. W\u00f3dkiewicz","year":"1984","unstructured":"W\u00f3dkiewicz, K.: Operational approach to phase-space measurements in quantum mechanics. Phys. Rev. Lett.\u00a052, 1064 (1984)","journal-title":"Phys. Rev. Lett."},{"key":"30_CR2","first-page":"102","volume":"11","author":"V.V. Kuryshkin","year":"1971","unstructured":"Kuryshkin, V.V.: On the construction of quantum operators. Izv. VUZov. Phys.\u00a011, 102\u2013106 (1971)","journal-title":"Izv. VUZov. Phys."},{"key":"30_CR3","first-page":"81","volume":"17","author":"V.V. Kuryshkin","year":"1972","unstructured":"Kuryshkin, V.V.: La m\u00e9canique quantique avec une fonction nonnegative de distribution dans 1\u2019espace des phases. Annales Inst. Henri Poincar\u00e9\u00a017, 81\u201395 (1972)","journal-title":"Annales Inst. Henri Poincar\u00e9"},{"key":"30_CR4","unstructured":"Kuryshkin, V.V.: Une g\u00e9n\u00e9ralisation possible de la m\u00e9canique quantique non relativiste. Compt. Rend. Acad. Sc. Paris 274 S\u00e9rie B, 1107\u20131110 (1972)"},{"key":"30_CR5","unstructured":"Kuryshkin, V.V.: L\u2019ossilateur harmonique \u00e0 une dimension dans la mecanique quantique a fonction de distribution non negative dans 1\u2019espace des phases. Compt. Rend. Acad. Sc. Paris 274 S\u00e9rie B, 1163\u20131165 (1972)"},{"key":"30_CR6","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/BF00713247","volume":"7","author":"V.V. Kuryshkin","year":"1973","unstructured":"Kuryshkin, V.V.: Some problems of quantum mechanics possessing a non-negative phase-space distribution function. Int. J. Theor. Phys.\u00a07, 451\u2013466 (1973)","journal-title":"Int. J. Theor. Phys."},{"issue":"1","key":"30_CR7","first-page":"62","volume":"6","author":"A.V. Zorin","year":"1998","unstructured":"Zorin, A.V., Kuryshkin, V.V., Sevastyanov, L.A.: Description of the spectrum of a hydrogen-like atom. Bull. PFUR. Ser. Phys.\u00a06(1), 62\u201366 (1998)","journal-title":"Bull. PFUR. Ser. Phys."},{"key":"30_CR8","first-page":"81","volume":"12","author":"A.V. Zorin","year":"2004","unstructured":"Zorin, A.V.: Approximate determination of states in quantum mechanics of Kuryshkin. Bull. PFUR, Ser. Physics\u00a012, 81\u201387 (2004)","journal-title":"Bull. PFUR, Ser. Physics"},{"issue":"1","key":"30_CR9","first-page":"121","volume":"3","author":"A.V. Zorin","year":"2004","unstructured":"Zorin, A.V.: The method of study of essential and discrete spectra of the Hamiltonian in quantum mechanics of Kuryshkin. Bull. PFUR, Ser. Appl. and Comp. Math.\u00a03(1), 121\u2013131 (2004)","journal-title":"Bull. PFUR, Ser. Appl. and Comp. Math."},{"key":"30_CR10","first-page":"497","volume-title":"Proc. CASC 2004","author":"A.V. Zorin","year":"2004","unstructured":"Zorin, A.V., Sevastianov, L.A., Belomestny, G.A., Laveev, E.B.: Quantum systems\u2019 modeling by methods of computer algebra. In: Proc. CASC 2004, pp. 497\u2013506. TUM Publ., Munich (2004)"},{"key":"30_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1007\/978-3-540-31852-1_75","volume-title":"Numerical Analysis and Its Applications","author":"A.V. Zorin","year":"2005","unstructured":"Zorin, A.V., Sevastianov, L.A., Belomestny, G.A.: Numerical search for the states with minimal dispersion in quantum mechanics with non\u2013negative quantum distribution function. In: Li, Z., Vulkov, L.G., Wa\u015bniewski, J. (eds.) NAA 2004. LNCS, vol.\u00a03401, pp. 613\u2013620. Springer, Heidelberg (2005)"},{"key":"30_CR12","doi-asserted-by":"publisher","first-page":"792","DOI":"10.1134\/S1063778807040229","volume":"70","author":"A.V. Zorin","year":"2007","unstructured":"Zorin, A.V., Sevastianov, L.A.: Hydrogen-like atom with nonnegative quantum distribution function. Nuclear Phys.\u00a070, 792\u2013799 (2007)","journal-title":"Nuclear Phys."},{"issue":"2","key":"30_CR13","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1134\/S0361768807020077","volume":"33","author":"A.V. Zorin","year":"2007","unstructured":"Zorin, A.V., Sevastianov, L.A., Tretyakov, N.P.: Computer modeling of hydrogen-like atoms in quantum mechanics with nonnegative distribution function. Programming and Computer Software\u00a033(2), 94\u2013104 (2007)","journal-title":"Programming and Computer Software"},{"key":"30_CR14","unstructured":"Gorbachev, A.V.: Modeling of Alkaline Metal Spectra using Quantum Mechanics with Nonnegative Quantum Distribution Function. Master\u2019s thesis. PFUR (2010) (in Russian)"},{"key":"30_CR15","unstructured":"Zorin, A.V., Sevastianov, L.A.: Kuryshkin-W\u00f3dkiewicz quantum measurements model. Bull. PFUR. Ser. Math. Inform. Phys.\u00a0(3), 99\u2013104 (2010)"},{"key":"30_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1007\/978-3-642-28212-6_17","volume-title":"Mathematical Modeling and Computational Science","author":"L. Sevastyanov","year":"2012","unstructured":"Sevastyanov, L., Zorin, A., Gorbachev, A.: Pseudo-differential operators in an operational model of the quantum measurement of observables. In: Adam, G., Bu\u0161a, J., Hnati\u010d, M. (eds.) MMCP 2011. LNCS, vol.\u00a07125, pp. 174\u2013181. Springer, Heidelberg (2012)"},{"key":"30_CR17","doi-asserted-by":"crossref","unstructured":"Ozawa, M.: Measurements of nondegenerate discrete observables. Phys. Rev. A 62, 062101(1\u201313) (2000)","DOI":"10.1103\/PhysRevA.62.062101"},{"key":"30_CR18","doi-asserted-by":"crossref","unstructured":"Ozawa, M.: Operations, disturbance, and simultaneous measurability. Phys. Rev. A 63, 032109(1\u201315) (2001)","DOI":"10.1103\/PhysRevA.63.032109"},{"key":"30_CR19","doi-asserted-by":"crossref","unstructured":"Ozawa, M.: Conservation laws, uncertainty relations, and quantum limits of measurements. Phys. Rev. Lett. 88, 050402(1\u20134) (2002)","DOI":"10.1103\/PhysRevLett.88.050402"},{"key":"30_CR20","doi-asserted-by":"publisher","first-page":"32106","DOI":"10.1103\/PhysRevA.78.032106","volume":"78","author":"G. Kimura","year":"2008","unstructured":"Kimura, G., Meister, B.K., Ozawa, M.: Quantum limits of measurements induced by multiplicative conservation laws: Extension of the Wigner\u2013Araki\u2013Yanase theorem. Phys. Rev. A\u00a078, 032106 (2008)","journal-title":"Phys. Rev. A"},{"key":"30_CR21","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1103\/PhysRev.120.622","volume":"120","author":"H. Araki","year":"1960","unstructured":"Araki, H., Yanase, M.M.: Measurement of quantum mechanical operators. Phys. Rev.\u00a0120, 622\u2013626 (1960)","journal-title":"Phys. Rev."},{"key":"30_CR22","doi-asserted-by":"publisher","first-page":"592","DOI":"10.1007\/s10701-010-9462-y","volume":"41","author":"M. Ozawa","year":"2011","unstructured":"Ozawa, M.: Quantum reality and measurement: A quantum logical approach. Foundations of Physics\u00a041, 592\u2013607 (2011), doi:10.1007\/s10701-010-9462-y","journal-title":"Foundations of Physics"},{"key":"30_CR23","first-page":"363","volume-title":"Proc. 8th Int. Conf. on Quantum Communication, Measurement and Computing","author":"M. Ozawa","year":"2007","unstructured":"Ozawa, M.: Simultaneous measurability of non-commuting observables and the universal uncertainty principle. In: Proc. 8th Int. Conf. on Quantum Communication, Measurement and Computing, pp. 363\u2013368. NICT Press, Tokyo (2007); Ozawa, M., Kitajima, Y.: Reconstructing Bohr\u2019s reply to EPR in algebraic quantum theory. Foundations of Physics 42(4), 475\u2013487 (2012), doi:10.1007\/s10701-011-9615-7"},{"key":"30_CR24","first-page":"113","volume":"61","author":"M. Ozawa","year":"2009","unstructured":"Ozawa, M.: Mathematical foundations of quantum information: Measurement and foundations. Sugaku\u00a061-2, 113\u2013132 (2009) (in Japanese)","journal-title":"Sugaku"},{"issue":"5","key":"30_CR25","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1063\/1.1704163","volume":"5","author":"C.L. Mehta","year":"1964","unstructured":"Mehta, C.L.: Phase-space formulation of the dynamics of canonical variables. J. Math. Phys.\u00a05(5), 677\u2013686 (1964)","journal-title":"J. Math. Phys."},{"issue":"2","key":"30_CR26","first-page":"81","volume":"11","author":"A.V. Zorin","year":"2003","unstructured":"Zorin, A.V., Sevastianov, L.A.: Mathematical modeling of quantum mechanics with non-negative QDF. Bull. PFUR. Ser. Phys.\u00a011(2), 81\u201387 (2003)","journal-title":"Bull. PFUR. Ser. Phys."},{"key":"30_CR27","first-page":"233","volume-title":"Adv. in Atomic and Molec. Phys.","author":"M. Rotenberg","year":"1970","unstructured":"Rotenberg, M.: Theory and applications of Sturmian functions. In: Bates, D.R., Esterman, I. (eds.) Adv. in Atomic and Molec. Phys., vol.\u00a06, pp. 233\u2013268. Academic Press, New York (1970)"},{"key":"30_CR28","doi-asserted-by":"publisher","DOI":"10.1142\/9789812773593","volume-title":"Generalised Sturmians and Atomic Spectra","author":"J. Avery","year":"2006","unstructured":"Avery, J.: Generalised Sturmians and Atomic Spectra. World Scientific, Singapore (2006)"},{"key":"30_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02055756","volume":"46","author":"H. Weyl","year":"1927","unstructured":"Weyl, H.: Quantenmechanik und Gruppentheorie. Zeitschrift f\u00fcr Physik\u00a046, 1\u201346 (1927)","journal-title":"Zeitschrift f\u00fcr Physik"},{"issue":"1","key":"30_CR30","first-page":"134","volume":"1","author":"L.A. Sevastianov","year":"2002","unstructured":"Sevastianov, L.A., Zorin, A.V.: The method of lower bounds for the eigenvalues of the Hamiltonian differential operator in quantum mechanics of Kuryshkin. Bull. PFUR, Ser. Appl. and Comp. Math.\u00a01(1), 134\u2013144 (2002)","journal-title":"Bull. PFUR, Ser. Appl. and Comp. Math."},{"key":"30_CR31","first-page":"169","volume-title":"Proc. Second Int. Conf. on Func. Anal. and Diff. Op.","author":"A.V. Zorin","year":"2003","unstructured":"Zorin, A.V., Sevastianov, L.A.: Spectral properties of the Hamilton operator in quantum mechanics with non-negative QDF. In: Proc. Second Int. Conf. on Func. Anal. and Diff. Op., pp. 169\u2013170. Fizmatlit-Publ., Moscow (2003)"},{"issue":"1","key":"30_CR32","first-page":"106","volume":"3","author":"A.V. Zorin","year":"2004","unstructured":"Zorin, A.V., Sevastianov, L.A., Belomestny, G.A.: Analytical calculation of observables\u2019 matrices of Hydrogen-like atom in Kuryshkin\u2019s Quantum Mechanics. Bull. PFUR, Ser. Appl. and Comp. Math.\u00a03(1), 106\u2013120 (2004)","journal-title":"Bull. PFUR, Ser. Appl. and Comp. Math."},{"key":"30_CR33","series-title":"Analysis of Operators","volume-title":"Methods of Modern Mathematical Physics","author":"M. Reed","year":"1977","unstructured":"Reed, M., Simon, B.: Methods of Modern Mathematical Physics. Analysis of Operators, vol.\u00a0IV. Academic Press, New York (1977)"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-02297-0_30","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T15:56:41Z","timestamp":1558022201000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-02297-0_30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783319022963","9783319022970"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-02297-0_30","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}