A COMPARISON THEOREM OF THE EIGENVALUE GAP FOR ONE-DIMENSIONAL BARRIER POTENTIALS

  • Hyun, Jung-Soon (Department of Mathematics, Yeungnam University)
  • Published : 2000.05.01

Abstract

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.

Keywords

Schrodinger operator;eigenvalue gap

References

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