Extension of a spectral bounding method to the PT invariant states of the -(iX)**N nonHermitian potential

Yan, Z.; Handy, C.R.

doi:10.1088/0305-4470/34/46/313

Extension of a spectral bounding method to the PT invariant states of the -(iX)**N nonHermitian potential

Z. Yan
(
- Clark Atlanta U.
)
,
C.R. Handy
(
- Clark Atlanta U.
)

Nov, 2001

16 pages

Published in:

J.Phys.A 34 (2001) 9907-9922

DOI:

10.1088/0305-4470/34/46/313

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Abstract: (IOP)

The eigenvalue moment method (EMM) developed by Handy (J. Phys. A: Math. Gen.200134L271,J. Phys. A: Math. Gen.2001345065). Handyet al(J. Phys. A: Math. Gen.2001345593), and Handy and Xiao-Qian Wang (J. Phys. A: Math. Gen.2001348297), which generates converging lower and upper bounds to the (complex) discrete state energies, is extended to the case of discrete states with non-Real support. In particular, Bender and Boettcher (Phys. Rev. Lett.1998805243) have argued on the reality of the discrete state spectrum for the −(iX)Npotential. ForN(integer) ≥ 4, such PT-invariant solutions can only exist on appropriate complex contours. We develop and apply the necessary EMM formalism to such cases. In particular, the restriction of EMM to theanti-Stokesangles significantly increases the convergence rate of the bounds.

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