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    on the number of bound states for the one-dimensional Schrodinger equation

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    Downloads: 298
    Date
    1998-09
    Author
    Aktosun, T.
    Klaus, M.
    van der Mee, C.
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    Abstract
    The number of bound states of the one-dimensional Schrodinger equation is analyzed in terms of the number of bound states corresponding to ''fragments'' of the potential. When the potential is integrable and has a finite first moment, the sharp inequalities 1 -p + Sigma(j=1)(p) N(j)less than or equal to N less than or equal to Sigma(j=1)(p) N-j are proved, where p is the number of fragments, N is the total number of bound states, and N-j is the number of bound states for the jth fragment. When p=2 the question of whether N=N-1 +N-2 or N=N-1+N-2-1 is investigated in detail. An illustrative example is also provided. (C) 1998 American Institute of Physics.
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    http://hdl.handle.net/10919/47072
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    • Faculty Works, Department of Mathematics [181]

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