On the Spectrum of Eigenparameter-Dependent Quantum Difference Equations
نویسندگان
چکیده
We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions depending on an eigenvalue parameter. Discussing the point spectrum and using the uniqueness theorem of analytic functions, we present a condition that guarantees that this BVP has a finite number of eigenvalues and spectral singularities with finite multiplicities.
منابع مشابه
Quadratic eigenparameter-dependent quantum difference equations
The main aim of this paper is to construct quantum extension of the discrete Sturm–Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. ...
متن کاملTime-dependent analysis of carrier density and potential energy in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD)
Interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. Numerical methods are commonly employed to study such systems. In this paper we investigate the numerical calculation of quantum transport of electrons in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD). The simulation is based on the imaginary time...
متن کاملModulation Response and Relative Intensity Noise Spectra in Quantum Cascade Lasers
Static properties, relatively intensity noise and intensity modulation response in quantum cascade lasers (QCLs) studied theoretically in this paper. The present rate equations model consists of three equations for the electrons density in the conduction band and one equation for photons density in cavity length. Two equations were derived to calculate the noise and modulation response. Calcula...
متن کاملTime-dependent analysis of carrier density and potential energy in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD)
Interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. Numerical methods are commonly employed to study such systems. In this paper we investigate the numerical calculation of quantum transport of electrons in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD). The simulation is based on the imaginary time...
متن کاملForm Domains and Eigenfunction Expansions for Differential Equations with Eigenparameter Dependent Boundary Conditions
Form domains are characterized for regular 2n-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the eigenparameter. Corresponding modes of convergence for eigenfunction expansions are studied, including uniform convergence of the first n− 1 derivatives.
متن کامل