Abstract
We study the discrete part of spectrum of a singular non-self-adjoint second-order differential equation on a semiaxis with an operator coefficient. Its boundedness is proved. The result is applied to the Schrödinger boundary value problem −Δu+q(x)u=λ2u, u|∂D=0, with a complex potential q(x) in an angular domain.
Keywords
Mathematics
Self-adjoint operator
Mathematical analysis
Spectrum (functional analysis)
Boundary value problem
Operator (biology)
Differential operator
Domain (mathematical analysis)
Discrete spectrum
Partial differential equation
Differential equation
Schrödinger equation
Mathematical physics
Physics
Quantum mechanics
Hilbert space
Eigenvalues and eigenvectors
Subject Areas
Differential Equations and Boundary Problems
·Applied Mathematics ·Physical Sciences
Spectral Theory in Mathematical Physics
·Mathematical Physics ·Physical Sciences
Advanced Mathematical Modeling in Engineering
·Computational Theory and Mathematics ·Physical Sciences
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