相互作用双费米子系统精确解与变分方法匹配的改进
Improvement of the matching of the exact solution and variational approaches in an interacting two-fermion system
摘要：
对一维简谐势中相互作用的两费米子系统的相对运动构造了一个更合理的试探基态波函数。在边界处，波函数及其一阶导数都是连续的，准动量由一个更实际的约束条件决定，该约束条件将两个变分参数联系起来。将变分原理应用于相对运动的哈密顿量对试探波函数的期望值，得到了基态能量的上界。结果表明，能量和波函数与解析解的一致性比原方案好。
英文摘要：
A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a 1D harmonic potential. At the boundaries both the wave function and its first derivative are continuous and the quasi-momentum is determined by a more practical constraint condition which associates two variational parameters. The upper bound of the ground state energy is obtained by applying the variational principle to the expectation value of the Hamiltonian of relative motion on the trial wave function. The resulted energy and wave function show better agreement with the analytical solution than the original proposal.
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