2,613 research outputs found
Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to
We show that a recently developed method for generating bounds for the
discrete energy states of the non-hermitian potential (Handy 2001) is
applicable to complex rotated versions of the Hamiltonian. This has important
implications for extension of the method in the analysis of resonant states,
Regge poles, and general bound states in the complex plane (Bender and
Boettcher (1998)).Comment: Submitted to J. Phys.
Generating Converging Bounds to the (Complex) Discrete States of the Hamiltonian
The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is
applied to the Hamiltonian, enabling
the algebraic/numerical generation of converging bounds to the complex energies
of the states, as argued (through asymptotic methods) by Delabaere and
Trinh (J. Phys. A: Math. Gen. {\bf 33} 8771 (2000)).Comment: Submitted to J. Phys.
Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential
Moment based methods have produced efficient multiscale quantization
algorithms for solving singular perturbation/strong coupling problems. One of
these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev.
Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging
lower and upper bounds to a specific discrete state energy, once the signature
property of the associated wavefunction is known. This method is particularly
effective for multidimensional, bosonic ground state problems, since the
corresponding wavefunction must be of uniform signature, and can be taken to be
positive. Despite this, the vast majority of problems studied have been on
unbounded domains. The important problem of an electron in an infinite quantum
lens potential defines a challenging extension of EMM to systems defined on a
compact domain. We investigate this here, and introduce novel modifications to
the conventional EMM formalism that facilitate its adaptability to the required
boundary conditions.Comment: Submitted to J. Phys.
Generating Converging Eigenenergy Bounds for the Discrete States of the -ix^3 Non-Hermitian Potential
Recent investigations by Bender and Boettcher (Phys. Rev. Lett 80, 5243
(1998)) and Mezincescu (J. Phys. A. 33, 4911 (2000)) have argued that the
discrete spectrum of the non-hermitian potential should be real.
We give further evidence for this through a novel formulation which transforms
the general one dimensional Schrodinger equation (with complex potential) into
a fourth order linear differential equation for . This permits the
application of the Eigenvalue Moment Method, developed by Handy, Bessis, and
coworkers (Phys. Rev. Lett. 55, 931 (1985);60, 253 (1988a,b)), yielding rapidly
converging lower and upper bounds to the low lying discrete state energies. We
adapt this formalism to the pure imaginary cubic potential, generating tight
bounds for the first five discrete state energy levels.Comment: Work to appear in J. Phys. A: Math & Ge
Eigenvalues of PT-symmetric oscillators with polynomial potentials
We study the eigenvalue problem
with the boundary
conditions that decays to zero as tends to infinity along the rays
, where is a polynomial and integers . We provide an
asymptotic expansion of the eigenvalues as , and prove
that for each {\it real} polynomial , the eigenvalues are all real and
positive, with only finitely many exceptions.Comment: 23 pages, 1 figure. v2: equation (14) as well as a few subsequent
equations has been changed. v3: typos correcte
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Benchmark full configuration-interaction calculations on HF and NH2
Full configuration-interaction (FCI) calculations are performed at selected geometries for the 1-sigma(+) state of HF and the 2-B(1) and 2-A(1) states of NH2 using both DZ and DZP gaussian basis sets. Higher excitations become more important when the bonds are stretched and the self-consistent field (SCF) reference becomes a poorer zeroth-order description of the wave function. The complete active space SCF - multireference configuration-interaction (CASSCF-MRCI) procedure gives excellent agreement with the FCI potentials, especially when corrected with a multi-reference analog of the Davidson correction
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