支持束缚态基本N重态的尖峰和PT对称十进势
Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states
摘要:
我们证明了具有中心尖峰V(x)= x^{10} + ax^8 + bx^6 + cx^4 + dx^2 + f/x^2的势阱具有任意有限多重态的初等精确束缚态. V(x)的强渐近增长意味着通过复杂的边界条件在PT对称量子化中的模糊性,但是三个合格的配方在我们的例外解处一致。
英文摘要:
We show that the potential wells with a central spike V(x) = x^{10} + a x^8 + b x^6+ c x^4 + d x^2 + f/x^2 possess arbitrary finite multiplets of elementary exact bound states. The strong asymptotic growth of V(x) implies an ambiguity in the PT-symmetric quantization via complex boundary conditions but the three eligible recipes coincide at our exceptional solutions.
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