Note on the kinetic energy inequality leading to Lieb's negative ionization upper bound |
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Authors: | Takashi Ichinose |
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Institution: | (1) Department of Mathematics, Faculty of Science, Kanazawa University, 920-11 Kanazawa, Japan |
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Abstract: | The kinetic energy inequality is alternatively proved which yields Lieb's boundN < 2Z + 1 on the maximum negative ionization of an atom with nucleus chargeZ andN electrons when the kinetic energy operator is the nonrelativistic or relativistic magnetic Schrödinger operator. It is seen to follow from the free case where the vector potential vanishes. The proof applies to the Weyl quantized relativistic magnetic Schrödinger operator as well.Research partially supported by Grant-in-Aid for Scientific Research Nos. 04640141 and 05640165, Ministry of Education, Science and Culture, Japanese Government. |
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Keywords: | 35J10 81V45 81V55 |
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