Finite element method for finite-size scaling in quantum mechanics.

We combined the finite-size scaling method with the finite element method to provide a systematic procedure for obtaining quantum critical parameters for a quantum system. We present results for the Yukawa potential solved with the finite element approach. The finite-size scaling approach was then used to find the critical parameters of the system. The critical values lambda c, alpha, and nu were found to be 0.83990345, 2.0002, and 1.002, respectively, for l = 0. These results compare well with the theoretically exact values for alpha and nu and with the best numerical estimations for lambda c. The finite element method is general and can be extended to larger systems.