대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제37권2호
  • /
  • Pages.353-360
  • /
  • 2000
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A COMPARISON THEOREM OF THE EIGENVALUE GAP FOR ONE-DIMENSIONAL BARRIER POTENTIALS

  • 발행 : 2000.05.01
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초록

The fundamental gap between the lowest two Dirich-let eigenvalues for a Schr dinger operator HR={{{{ { { d}^{2 } } over { { dx}^{2 } } }}}}+V(x) on L({{{{ LEFT | -R,R RIGHT | }}}}) is compared with the gap for a same operator Hs with a different domain {{{{ LEFT [ -S,S RIGHT ] }}}} and the difference is exponentially small when the potential has a large barrier.

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참고문헌

  1. Proc. A.M.S. v.105 Optimal Lower Bound for the Gap Between the First Two Eigenvalues of One-dimensional Schrodinger Operators with Symmetric Single-well Potentials M. Ashbaugh;R. Benguria
  2. Theory of Ordinary Differential Equations E. Coddington;N. Levinson
  3. Comm. Math. Phys. v.75 Double wells E. HarrellⅡ
  4. General bounds for the eigenvalues of Schrodinger operators in Conference on Maximum principles and eigenvalue problems in partial differential equations University of Tennessee
  5. J. Math. Anal. Appl. v.221 Decay for Barrier Potentials J. Hyun
  6. Comm. Math. Phys. v.97 Universal Lower Bounds on Eigenvalue Splitting for One-dimensional Schrodinger Operators W. Kirsh;B. Simon
  7. Proc. A.M.S. v.121 The Eigenvalue Gap for One-dimensional Convex Potential R. Lavine