标题： 量子理论中的一个新的广义逼近方案(NGAS):应用于非谐振子和双井振子 显示英文标题

标题： A new general approximation scheme(NGAS) in quantum theory:application to the anharmonic- and double well oscillators

摘要： 提出了一种新的量子理论近似方案，该方案有潜力适用于任意相互作用系统。 该方法在于将原来的哈密顿量近似为一个对应于适当可精确求解系统的哈密顿量（具有相互作用），使得两者的“量子平均”相等，从而强制自洽性。该方法超越了变分法和微扰论的局限性。通过构建一种改进的微扰理论（IPT），可以系统地改进结果，这种理论自动满足收敛条件。 对于四次、六次和八次非谐振子以及四次和六次双井振子的情况，得到了一致准确的结果。 首阶结果重现了不同方法和不同输入假设下先前的结果。六次振子的结果与超对称的精确预测吻合良好。 我们还讨论了近似的有效真空态的稳定性和结构。 显示英文摘要

摘要： A new scheme of approximation in quantum theory is proposed which is potentially applicable to arbtrary interacting systems. The method consists in in approximating the original Hamiltonian by one corresponding to a suitable exactly solvable system (with interaction) such that the "quantum average" of both are equal, thus forcing self-consistency.The method transcends the limitations of the variational method and the perturbation theory.The results are systematically improvable by the construction of a improved perturbation theory (IPT) which automatically satisfies the condition of convergence. Uniformly accurate results are obtained for the case of the quartic-,sextic- and octic anharmonic oscillators as well as the quartic and sextic double well oscillators. The leading order results reproduce earlier results by different methods using different input assumptions.The results for the sextic oscillators agree well with exact prediction of supersymmetry. We also discuss the stability and structure of the effective vacuum state of the approximation.