2021/06/14 by Behrndt, Jussi, Khrabustovskyi, Andrii
#34L05 #34L40 #81Q10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2106.07184
The paper deals with singular Schrödinger operators of the form -d2\over d x2 + ∑k∈ℤ γk δ(⋅-zk), γk∈ℝ, in L2(ℓ-,ℓ+), where (ℓ-,ℓ+) is a bounded interval, and δ(⋅-zk) is the Dirac delta-function supported at zk∈ (ℓ-,ℓ+). It will be shown that the interaction strengths γk and the points zk can be chosen in such a way that the essential spectrum and a bounded part of the discrete spectrum of this self-adjoint operator coincide with prescribed sets on a real line.