基态球谐振子的空间“塌陷”

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

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 .

A rigorous solution of Schrodinger equation of an sphere-symmetry harmonic oscillator is studied by the power series method. We found that wave function psi(r, theta, phi) vertical bar (r - 0) can be infinite, r psi(r, theta, phi) vertical bar (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 k omega/2. The space dent will appear in the ground state of the sphere-symmetry harmonic oscillator.