  A classical computer simulating Schrodinger dynamics of a quantum system
requires resources which scale exponentially with the size of the system, and
is regarded as inefficient for such purposes. However, a quantum computer made
up of a controllable set of quantum particles has the potential to efficiently
simulate other quantum systems of matching dimensions. In this work we studied
quantum simulations of single particle Schrodinger equation for certain
one-dimensional potentials. In particular, we report the following cases: (i)
spreading of wave-function of a free-particle, (ii) evolution of a particle in
a potential-well, and (iii) reflection of a particle from a potential-barrier.
Using a five-qubit NMR system, we achieve space discretization with four
qubits, and the other qubit is used for preparation of initial states as well
as measurement of spatial probabilities. The experimental relative
probabilities compare favorably with the theoretical values, thus effectively
mimicking a small-scale quantum simulator.
