Approximations of spectra of Schrodinger operators with complex potentials on (d)

作者：Boegli Sabine; Siegl Petr; Tretter Christiane^*

来源：Communications in Partial Differential Equations, 2017, 42(7): 1001-1041.

DOI：10.1080/03605302.2017.1330342

• Complex potential
• domain truncation
• eigenvalue approximation
• harmonic oscillator
• Laplace operator
• non-selfadjoint Schrodinger operator
• pseudospectra
• resolvent convergence
• spectral exactness
• spectral pollution
• spurious eigenvalue
• 35J10
• 35P05
• 47A10
• 47A58
• 81Q15

We study spectral approximations of Schrodinger operators T=-+Q with complex potentials on =(d), or exterior domains < subset of>(d), by domain truncation. Our weak assumptions cover wide classes of potentials Q for which T has discrete spectrum, of approximating domains (n), and of boundary conditions on (n) such as mixed Dirichlet/Robin type. In particular, Re Q need not be bounded from below and Q may be singular. We prove generalized norm resolvent convergence and spectral exactness, i.e. approximation of all eigenvalues of T by those of the truncated operators T(n)without spectral pollution. Moreover, we estimate the eigenvalue convergence rate and prove convergence of pseudospectra. Numerical computations for several examples, such as complex harmonic and cubic oscillators for d=1,2,3, illustrate our results.

• 出版日期2017