基态球谐振子的空间“塌陷”

用幂级数方法研究球谐振子定态薛定谔方程解析解，发现波函数球系表示ψ(r,θ，φ)在r～0处可以无界，只要rψ(r,θ，φ)在r～0处有界，就不违背波函数的玻恩统计解释而且基态能量是ω/2, 而不是3ω/2，这是低能量条件下的振动系统空间“塌陷”现象. 关键词： 球谐振子 基态能量 波函数 空间塌陷

The space dent of sphere-symmetry harmonic oscillator in ground state

A rigorous solution of Schrdinger equation of an sphere symmetry harmonic oscillator is studied by the power series method.We found that wave function ψ(r,θ,φ)|r～0 can be infinite, rψ(r,θ,φ)|r～0 must be finite; this is in accord with Born's statistical explanation. The ground state energy of the sphere symmetry harmonic oscillator is ω/2. The space dent will appear in the ground state of the sphere symmetry harmonic oscillator.