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(Quasi)-Convexification of Barta's (Multi-Extrema) Bounding Theorem

Autor: Handy, C. R.

There has been renewed interest in the exploitation of Barta's configuration space theorem (BCST, (1937)) which bounds the ground state energy. Mouchet's (2005) BCST analysis is based on gradient optimization (GO). However, it overlooks significant d

Externí odkaz: http://arxiv.org/abs/math-ph/0510071

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Comment on the article by Bender et al, J. Phys. A 35, L467 (2002)

Autor: Handy, C. R.

The recent Letter by Bender, Berry, and Mandilara (2002, BBM) presents some interesting symmetry arguments which enable one to transform non-hermitian, PT invariant, (complex) polynomial potential hamiltonians, into secular equation representations w

Externí odkaz: http://arxiv.org/abs/math-ph/0208021

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Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to $p^2-ix^3$

Autor: Handy, C. R., Wang, Xiao Qian

We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-ix^3$ potential (Handy 2001) is applicable to complex rotated versions of the Hamiltonian. This has important implications for extens

Externí odkaz: http://arxiv.org/abs/math-ph/0105019

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Generating Converging Bounds to the (Complex) Discrete States of the $P^2 + iX^3 + i\alpha X$ Hamiltonian

Autor: Handy, C. R.

The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is applied to the $H_\alpha \equiv P^2 + iX^3 + i\alpha X$ Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the $L^2$ sta

Externí odkaz: http://arxiv.org/abs/math-ph/0104036

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Multiscale Reference Function Analysis of the ${\cal P}{\cal T}$ Symmetry Breaking Solutions for the $P^2+iX^3+i\alpha X$ Hamiltonian

Autor: Handy, C. R., Khan, D., Wang, Xiao-Qian, Tymczak, C. J.

The recent work of Delabaere and Trinh (2000 J. Phys. A 33 8771) discovered the existence of ${\cal P}{\cal T}$-symmetry breaking, complex energy, $L^2$ solutions for the one dimensional Hamiltonian, $P^2+iX^3+i\alpha X$, in the asymptotic limit, $\a

Externí odkaz: http://arxiv.org/abs/math-ph/0104037

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Generating Converging Eigenenergy Bounds for the Discrete States of the -ix^3 Non-Hermitian Potential

Autor: Handy, C. R.

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 $V(x) = -ix^3$ should be real. We give further evidence

Externí odkaz: http://arxiv.org/abs/math-ph/0104035

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A Nonperturbative Perspective on Inner Product Quantization: Highly Accurate Solutions to the Schr{\'o}dinger Equation

Autor: Tymczak, C. J., Japaridze, G. S., Handy, C. R., Wang, Xiao-Qian

We devise a new and highly accurate quantization procedure for the inner product representation, both in configuration and momentum space. Utilizing the representation $\Psi(\xi) = \sum_{i}a_i[E]\xi^i R_{\beta}(\xi)$, for an appropriate reference fun

Externí odkaz: http://arxiv.org/abs/quant-ph/9707005

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