2010 Fiscal Year Final Research Report
Study on quantum mechanical propagators and path integrals
| Project/Area Number |
20540161
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2010
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| Keywords | 量子力学 / プロパゲイター / 経路積分 / グリーン関数 / 熱核 / トロター積公式 / 相対論的シュレーディンガー作用素 / ディラック作用素 |
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| Research Abstract |
This research concerns the quantum-mechanical propagator, namely, the integral kernel of the Schrodinger unitary group, Green function as well as their imaginary-time version, the integral kernel of the Schrodinger semi-group and heat kernel. Results are obatined among others on the following two topics. One is to investigate how good an approximation is given to the integral kernel of the Schrodinger semi-group or heat kernel by path integral based on the operator-norm selfadjoint Trotter product formulas obtained, and the other is to revisit with some new aspects the problem on the imaginary-time path integral representation for three relativistic Schrodinger operators.
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