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The hydrodynamical formulation of quantum mechanics and the two-dimensional parabolic potential barrier
http://hdl.handle.net/2241/6885
http://hdl.handle.net/2241/6885c1539bf8-e837-4c63-8d07-22ccdfba0c88
名前 / ファイル | ライセンス | アクション |
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A2845.pdf (176.8 kB)
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1.pdf (383.6 kB)
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Item type | Thesis or Dissertation(1) | |||||
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公開日 | 2007-07-25 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | The hydrodynamical formulation of quantum mechanics and the two-dimensional parabolic potential barrier | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_db06 | |||||
タイプ | doctoral thesis | |||||
アクセス権 | ||||||
アクセス権 | open access | |||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||
著者 |
新堀, 敏基
× 新堀, 敏基 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | THE dissertation deals with the two-dimensional isotropic parabolic potential barrier as a solvable model of a two-dimensional unstable system in non-relativistic quantum mechanics. The time-independent Schrodinger equation for this model is set up as the eigenvalue problem in Gel'fand triplet and its exact solutions are expressed by generalized eigen-functions belonging to complex energy eigenvalues. There are stationary states with a real energy eigenvalues. There are statinary states with a real energy eigenvalue involved in those solutions, and they are infinitely degenerate. A physical picture of the generalized eigenstates of the unstable system is obtained from the hydrodynamical point of view. For the first few stationary states of the two-dimensional parabolic potential barrier, the complex velocity potentials in the hydrodynamical formulation of quantum mechanics express the two-dimensional irrotational flows round a right angle. We find that this result can be deduced from the general connection between complex velocity potentials and singular potentials in two-dimensional quantum systems. | |||||
言語 | en | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | Includes bibliographical references | |||||
言語 | en | |||||
書誌情報 |
発行日 2002 |
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取得学位 | ||||||
学位名 | 博士(理学) | |||||
取得学位 | ||||||
学位名 | Doctor of Philosophy in Science | |||||
学位授与大学 | ||||||
学位授与機関識別子Scheme | kakenhi | |||||
学位授与機関識別子 | 12102 | |||||
言語 | ja | |||||
学位授与機関名 | 筑波大学 | |||||
言語 | en | |||||
学位授与機関名 | University of Tsukuba | |||||
学位授与年度 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 2001 | |||||
学位授与年月日 | ||||||
学位授与年月日 | 2002-03-25 | |||||
報告番号 | ||||||
学位授与番号 | 甲第2845号 |