产生-ix^3非厄米特势离散态的收敛本征能界
Generating Converging Eigenenergy Bounds for the Discrete States of the -ix^3 Non-Hermitian Potential
摘要：
Bender和Boettcher（Phys. Rev. Lett 80，5243（1998））和Mezincescu（J. Phys. A.J. 33，4911（2000））已经论证了非厄米势$V(x) = -ix^3$的离散谱应该是实的。我们给出了进一步的证据，通过一个新的配方，将一般的一维薛定谔方程（复势）到一个四阶线性微分方程$|Ψ(x)|^2$。这允许应用特征值矩法，由Handy，Bessis和同事（物理学评论快报）开发。55，931（1985）;60，253（1988 a，b）），得到快速收敛的低离散态能量的下限和上限。我们适应这种形式主义的纯虚立方势，产生紧密的边界的前五个离散态能级。
英文摘要：
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 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 $|Ψ(x)|^2$. 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.
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