The density matrix renormalization group applied to single-particle quantum mechanics

A simplified version of White's density matrix renormalization group (DMRG) algorithm has been used to find the ground state of the free particle on a tight-binding lattice. We generalize this algorithm to treat the tight-bin ding particle in an arbitrary potential and to find excited states. We ther eby solve a discretized version of the single-particle Schrodinger equation , which we can then take to the continuum limit. This allows us to obtain v ery accurate results for the lowest energy levels of the quantum harmonic o scillator, anharmonic oscillator and double-well potential. We compare the DMRG results thus obtained with those achieved by other methods.