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<top_article>
<mrnumber>MR2730626</mrnumber>
<author>Hiroaki NIIKUNI</author>
<author_utf8>Hiroaki NIIKUNI</author_utf8>
<title>On the Location of the Degenerate Spectral Gaps of the Generalized Kronig-Penney Hamiltonians</title>
<journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
<volume>53</volume>
<year>2010</year>
<page>311--330</page>
<url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/53-2/53_311.pdf</url_pdf>
<mathsci_link>http://www.ams.org/mathscinet-getitem?mr=MR2730626</mathsci_link>
<abstract>We discuss the one-dimensional Schr&#246;dinger operators with two generalized point interactions in the basic period cell $[0,2\pi)$. In this paper, we investigate the coexistence problem for them. Namely, we analyze the set of the position of the degenerate spectral gaps.</abstract>
<keywords>Kronig-Penney Hamiltonian, Generalized point interaction, Band structure, Spectral gap, Cramer's formula, Monodromy matrix.</keywords>
<subject>34L15,34B30, 34L05, 34B37.</subject>
<fesi_info>
  <FILE>53-311</FILE>
  <YEAR>2010</YEAR>
  <TITLE>On the Location of the Degenerate Spectral Gaps of the Generalized Kronig-Penney Hamiltonians</TITLE>
  <AUTHOR>Hiroaki NIIKUNI</AUTHOR>
  <AUTHOR_utf8>Hiroaki NIIKUNI</AUTHOR_utf8>
</fesi_info>

<references>

<book>
<bibitem>1</bibitem>
<author>Albeverio, S.; Gesztesy, F.; H&#248;egh-Krohn, R.; Holden, H.</author>
<booktitle>Solvable models in quantum mechanics</booktitle>
<publisher>2nd ed., AMS Chelsea publishing, Rhode Island</publisher>
<year>2005</year>
<mr>MR2105735</mr>
</book>

<book>
<bibitem>2</bibitem>
<author>Albeverio, S.; Kurasov, P.</author>
<booktitle>Singular Perturbations of Differential Operators</booktitle>
<publisher>London Mathematical Society Lecture Note Series, 271, Cambridge Univ. Press</publisher>
<year>1999</year>
<mr>MR1752110</mr>
</book>

<article>
<bibitem>3</bibitem>
<author>Chernoff, P. R.; Hughes, R. J.</author>
<title>A new class of point interactions in one dimension</title>
<journal>J. Funct. Anal.</journal>
<vol>111</vol>
<year>1993</year>
<page>97-117</page>
<mr>MR1200638</mr>
</article>

<article>
<bibitem>4</bibitem>
<author>Gesztesy, F.; Holden, W.; Kirsch, W.</author>
<title>On energy gaps in a new type of analytically solvable model in quantum mechanics</title>
<journal>J. Math. Anal. Appl.</journal>
<vol>134</vol>
<year>1988</year>
<page>9-29</page>
<mr>MR0958850</mr>
</article>

<article>
<bibitem>5</bibitem>
<author>Hughes, R. J.</author>
<title>Generalized Kronig-Penney Hamiltonians</title>
<journal>J. Math. Anal. Appl.</journal>
<vol>222</vol>
<year>1998</year>
<page>151-166</page>
<mr>MR1623887</mr>
</article>

<book>
<bibitem>6</bibitem>
<author>Kittel, C.</author>
<booktitle>Introduction to solid state physics</booktitle>
<publisher>5th ed., Wiley, New York</publisher>
<year>1976</year>
<mr></mr>
</book>

<article>
<bibitem>7</bibitem>
<author>Kurasov, P.; Larson, J.</author>
<title>Spectral Asymptotics for Schr&#246;dinger operators with periodic point interactions</title>
<journal>J. Math. Anal. Appl.</journal>
<vol>266</vol>
<year>2002</year>
<page>127-148</page>
<mr>MR1876773</mr>
</article>

<article>
<bibitem>8</bibitem>
<author>Kronig, R.; Penney, W.</author>
<title>Quantum mechanics in crystal lattices</title>
<journal>Proc. Royal. Soc. London</journal>
<vol>130</vol>
<year>1931</year>
<page>499-513</page>
<mr></mr>
</article>

<book>
<bibitem>9</bibitem>
<author>Magnus, W.; Winkler, S.</author>
<booktitle>Hill's Equation</booktitle>
<publisher>Wiley</publisher>
<year>1966</year>
<mr>MR0197830</mr>
</book>

<article>
<bibitem>10</bibitem>
<author>Niikuni, H.</author>
<title>Identification of the absent spectral gaps in a class of generalized Kronig-Penney Hamiltonians</title>
<journal>Tsukuba J. Math.</journal>
<vol>31</vol>
<year>2007</year>
<page>39-65</page>
<mr>MR2337119</mr>
</article>

<article>
<bibitem>11</bibitem>
<author>Niikuni, H.</author>
<title>The rotation number for the generalized Kronig-Penney Hamiltonians</title>
<journal>Ann. Henri Poincar&#233;</journal>
<vol>8</vol>
<year>2007</year>
<page>1279--1301</page>
<mr>MR2360437</mr>
</article>

<article>
<bibitem>12</bibitem>
<author>Niikuni, H.</author>
<title>Absent spectral gaps of the generalized Kronig-Penney Hamiltonians</title>
<journal>Kyushu J. Math.</journal>
<vol>62</vol>
<year>2008</year>
<page>89-105</page>
<mr>MR2413785</mr>
</article>

<article>
<bibitem>13</bibitem>
<author>&#352;eba, P.</author>
<title>The generalized point interaction in one dimension</title>
<journal>Czech J. Phys. B</journal>
<vol>36</vol>
<year>1986</year>
<page>667-673</page>
<mr>MR0858618</mr>
</article>

<article>
<bibitem>14</bibitem>
<author>Yoshitomi, K.</author>
<title>Spectral gaps of the one-dimensional Schr&#246;dinger operators with periodic point interactions</title>
<journal>Hokkaido Math. J.</journal>
<vol>35</vol>
<year>2006</year>
<page>365-378</page>
<mr>MR2254656</mr>
</article>

</references>
</top_article>
