On the number of eigenvalues of Schrödinger operators with complex potentials

Abstract

Abstract. We study the eigenvalues of Schrödinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.

Asymptotic completeness in dissipative scattering theory

“…Assuming (6.2), it is known that H has only finitely many eigenvalues with finite algebraic multiplicities. See, e.g., [20] and references therein. In particular, Hypothesis 2.2 is satisfied.…”

Some Remarks on Upper Bounds for Weierstrass Primary Factors and Their Application in Spectral Theory

“…where R p is an explicitly known constant and a n (K) denotes the nth approximation number of K. For other appearances of Γ p in eigenvalue estimates (sometimes with a different notation), see, e.g. [4,8,12,25,22,9,11,16,32,13,24,14,15,17,23]. The results from below will allow us to compute the Γ p 's numerically (apparently, this has not been done before).…”

Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues

“…The condition (3) for Ω = (0, ∞) is sharp; Pavlov [16] proved that it cannot be relaxed to sup x∈(0,∞) |V (x)|e εx β < ∞ for any β ∈ 0, 1 2 . For an arbitrary odd dimension d, see [9] and the references therein for conditions guaranteeing a finite number of eigenvalues. We employ the following notation and conventions.…”