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采用重归一化Numerov算法求解关于超低温双原子碰撞问题的非含时薛定谔方程组. 以 39K- 133Cs碰撞为例, 研究了超低温下双原子Feshbach共振的性质. 结果表明, 重归一化Numerov算法可以很精确地描述超冷条件下碰撞过程. 与改进的logarithmic derivative算法相比, 在同等参数条件下, 重归一化Numerov方法在计算效率上虽然有一定劣势, 但在大格点步长参数范围内有着更好的稳定性. 提出重归一化Numerov和logarithmic derivative算法相结合的传播方法, 在保证结果精度的同时大大减少了计算时间. 此项算法也可以应用于求解任意温度下的两体碰撞耦合薛定谔方程组.
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关键词:
- 重归一化Numerov方法/
- 超低温/
- Feshbach共振
The renormalized Numerov algorithm is applied to solving time-independent Schrödinger equation relating to atom-atom collisions at ultralow temperature. The proprieties of Feshbach resonance in 39K- 133Cs collisions are investigated as an example. The results show that the renormalized Numerov method can give excellent results for ultracold colliding process. In contrast to improved log derivative method, the renormalized Numerov method displays a certain weakness in computational efficiency under the same condition. However, it is much stable in a wide range of grid step size. Hence a new propagating method is proposed by combining renormalized Numerov and logarithmic derivative method which can save computational time with a better accuracy. This algorithm can be used to solve close-coupling Schrödinger equation at arbitrary temperature for two-body collisions.[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] -
RN LOGD B0/G ΔB/G abg B0/G ΔB/G abg $ \begin{gathered} \left| {{f_{\text{K}}} = 1, \;{m_{f{\text{K}}}} = 1} \right\rangle + \\ \left| {{f_{{\text{Cs}}}} = 3, \;{m_{f{\text{Cs}}}} = 3} \right\rangle \\ \end{gathered} $ 341.89 4.8 79.1a0 341.90 4.8 79.0a0 421.35 0.4 74.7a0 421.36 0.4 74.7a0 831.14 4 × 10–4 80.9a0 831.14 3 × 10–4 81.0a0 860.50 0.05 82.1a0 860.52 0.05 82.0a0 915.57 1.2 80.2a0 915.56 1.2 80.1a0 
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ΔR NRN NLOGD $ B_0^{\rm error} $/G 0.004a0 4251 1990 0.02 0.006a0 2834 1990 0.11 0.008a0 2126 1990 0.57 0.010a0 1701 1990 2.31 下载:
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