A uniqueness theorem for higher order anharmonic oscillators

  • Søren Fournais

    University of Aarhus, Denmark
  • Mikael Persson Sundqvist

    Lund University, Sweden

Abstract

We study for αR\alpha\in\mathbb R,kN{0}k \in {\mathbb N} \setminus \{0\} the family of self-adjoint operators

d2dt2+(tk+1k+1α)2-\frac{d^2}{dt^2}+\Bigl(\frac{t^{k+1}}{k+1}-\alpha\Bigr)^2

in L2(R)L^2(\mathbb R) and show that if kk is even then α=0\alpha=0 gives the unique minimum of the lowest eigenvalue of this family of operators. Combined with earlier results this gives that for any k1k \geq 1, the lowest eigenvalue has a unique minimum as a function of α\alpha.

Cite this article

Søren Fournais, Mikael Persson Sundqvist, A uniqueness theorem for higher order anharmonic oscillators. J. Spectr. Theory 5 (2015), no. 2, pp. 235–249

DOI 10.4171/JST/96