一类环状球谐振子势Klein-Gordon方程的束缚态解

Bound state solutions of the Klein-Gordon equation with a new ring-shaped harmonic oscillator potential

提出了一种新的环状球谐振子势.在标量势与矢量势相等条件下,应用因子分解方法,求解了零自旋粒子在其中满足的Klein-Gordon方程,得到了束缚态解和能谱方程.归一化角向波函数和径向波函数分别以初等函数表示,并用笛卡尔符号法则讨论了能谱方程.结果表明,粒子在这一势场中惟一地具有正的分立能量本征值.

A new ring-shaped harmonic oscillator potential is proposed. Under the condition of equal scalar and vector potentials, the exact bound state solutions and the energy spectrum of the KleinGordon equation with this oscillator potential are obtained by the factorization method. It is shown that both the angular and radial wave functions are expressed in terms of the elementary functions respectively. The energy equation is analyzee with the Descarte＇s rule of signs and it is shown that for given values of M and n only discrete, positive energies are allowed.