用变分路径积分四阶测度方法处理量子力学双势阱问题

FOURTH-ORDER MEASURE APPROACH TO PROBLEMS OF QUANTUM DOUBLE-WELL POTENTIAL

提出了一种计算量子力学路径积分的四阶测度方法 ,其中势场的二阶和四阶导数为 2个变分参数。将此方法应用于双势阱问题 ,导出了有效经典势公式 .对自由能、有效经典势和能量劈裂进行了数值研究 ,获得了优于Feynman Kleinert二阶高斯测度方法的结果 .该方法克服了涨落模积分在跨越温度附近发散的困难 ,可以给出丰富的鞍点行为 ,尤其适合于位垒动力学 .

A fourth order measure approach for the variational path integrals is proposed and applied to the quantum double well potential. The expression of effective classical potential of the double well potential is derived. This approach can avoid the divergent path integral near the crossover temperature. The effective classical potential, free energy and level splitting are calculated numerically, the present results are better than that of Feynman Kleinert second order variational path integral method.