A new adaptive basis set based on the element-free Galerkin method (EFGM) for the quantum-mechanical calculation is proposed. In this method, wavefunctions are constructed on the basis of moving least-square (MLS) interpolation. Adaptivity is introduced by adjusting node distribution and associated parameters to nature of the solution, or distribution of zero and stationary points of the target wavefunction. Applications of the adaptive EFGM (AEFGM) to eigenvalue problems of one-dimensional harmonic oscillator and double-well potential systems are presented to demonstrate its effectiveness.
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