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| 005 | 20231030040800.0 | ||
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| 100 | _a20160408d2015 k y0rusy50 ba | ||
| 101 | 0 | _aeng | |
| 102 | _aCN | ||
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_aApplication of Advanced Divergent Series Summation Techniques forMolecule Vibrational Energy Spectrum Calculations. Analytical Properties of Complex-valued Energy Function of Different Molecules _fA. N. Duchko |
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| 203 |
_aText _celectronic |
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| 300 | _aTitle screen | ||
| 330 | _aThe Rayleigh-Schrödinger perturbation theory is applied to energy levels calculation of excited vibrational states for different molecules. The calculations are carried out for the vibrational states that correspond to three- to seven-fold vibrational excitations. Perturbation series diverge in the case of strong resonance interactions. Nevertheless, considering vibrational energy of each excited state not as a real number, but as a complex function and applying corresponding analytical functions theory, we were able not only to get the exact value of energy, but to find the reason of divergence, and to choose the best summation technique. Our summation technique is based on high-order Pade-Hermite approximations. Further research shows that series behavior completely depends on the singularities of complex energy function inside unit circle. This analysis helped us to make the first exact definition of resonance interaction and to develop a unique technique for vibrational energy spectrum calculations avoiding resonances. | ||
| 463 |
_t8th International Congress on Industrial and Applied Mathematics, China, August 10-14, 2015 _oProgram and Abstracts _v[CP-Th-E-62-5] _d2015 |
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| 610 | 1 | _aэлектронный ресурс | |
| 610 | 1 | _aтруды учёных ТПУ | |
| 700 | 1 |
_aDuchko _bA. N. _cmathematician _cAssistant of Tomsk Polytechnic University _f1990- _gAndrey Nikolaevich _2stltpush _3(RuTPU)RU\TPU\pers\32998 |
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| 712 | 0 | 2 |
_aНациональный исследовательский Томский политехнический университет (ТПУ) _bИнститут международного образования и языковой коммуникации (ИМОЯК) _bКафедра междисциплинарная (МД) _h3526 _2stltpush _3(RuTPU)RU\TPU\col\19012 |
| 801 | 2 |
_aRU _b63413507 _c20160408 _gRCR |
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| 856 | 4 | _uhttp://www.iciam2015.cn/Program%20&%20Abstracts.pdf#page=285 | |
| 942 | _cCF | ||