Virginia TechAktosun, T.Klaus, Martinvan der Mee, Cornelis2014-04-092014-04-091998-09Aktosun, T.; Klaus, M.; van der Mee, C., "On the number of bound states for the one-dimensional Schrödinger equation," J. Math. Phys. 39, 4249 (1998); http://dx.doi.org/10.1063/1.5325100022-2488http://hdl.handle.net/10919/47072The 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.en-USIn Copyrightinverse scatteringfactorizationpotentialsmatrixlineArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/39/9/10.1063/1.532510https://doi.org/10.1063/1.532510