二维非谐振子的束缚态解

Bound State Solutions of the Spiked Harmonic Oscillator in Two Dimensions

讨论势函数为V(ρ)=2ρ+λρα的非谐振子的Schr dinger方程。当α=2时其有Hamiltonian量的精确束缚态解。当α3时其有Hamiltonian量的微扰解,尤其是它的一阶、两阶的能量修正及零级、一级波函数。

In this paper we discuss in detail the two-dimensional Schr6dinger with the potentialV（ρ）=ρ^2＋λ/ρ^α.Theexaet bound state solutions are obtained when a = 2 . The perturbative solutions are also given when α≥3,which especially contain the first-order and second-order revised energy and the zero-order and one-order wavefunction.