Separation of variables in perturbed cylinders

We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-to-one mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to an equivalent problem for an operator with variable coefficients. Taking advantage of the simple geometry we separate variables by means of the Fourier decomposition method. The ODE system obtained in this way is then solved numerically yielding the eigenvalues of the operator. The same approach allows us to find complex resonances arising in some non-compact domains. We discuss numerical examples related to quantum waveguide problems.Comment: LaTeX 2e, 18 pages, 6 figure

Multi-reference coupled-cluster methods for ionization potentials with partial inclusion of triple excitations

An extension of multi-reference coupled-cluster (MRCC) methods to include some effects of triple excitations for the direct calculation of ionization potentials is presented. A series of non-iterative methods are proposed, derived in analogy to the successful non-iterative inclusions of triple excitations for ground states. Results of two of these methods, MRCCSD+T(3) and MRCCSD+T∗(3) are presented for N2, H2CO, and CH2(1A1). We also consider how ionization potentials vary with alternative ways of determining the correlated ground state