arXiv subjects

Brian L Burrows

Publications and source records attributed to Brian L Burrows.

2 recordsLinked to original sources

arXiv2024

Solutions of time-dependent Schrodinger equations for model non-Hermitian quantum mechanical systems

The time-dependent Schrodinger equation is solved for two model problems for a non-Hermitian quantum system.A simple matrix model system is used to examine two critical problems for these systems: complex and non-observable energies and situations where the matrix is defective. In addition the stationary states for infinite dimensional model system, which is confined in space , is examined and it is shown that the pattern of eigenvalue energies differs from when the system is unconfined.

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arXiv2023

Solutions of some Schrodinger equations

Two types of non-Hermitian systems are considered. One of them is both non-Hermitian and non-Linear and an iterative process is used to obtain excited state solutions; the ground state may be solved exactly. The model has been used in many physical systems and the method of calculation uses a simple Hilbert space with a generalised inner product. The second type has a complex term in the Hamiltonian and is a well studied problem in the infinite interval. Here a finite interval is considered and a complete set of eigenfunctions for this interval is used.The relationship between the finite interval states and the infinite interval states is discussed.

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