  In this paper, we implement a quantum algorithm -on IBM quantum devices, IBM
QASM simulator and PPRC computer cluster -to find the energy values of the
ground state and the first excited state of a particle in a finite square-well
potential. We use the quantum phase estimation technique and the iterative one
to execute the program on PPRC cluster and IBM devices, respectively. Our
results obtained from executing the quantum circuits on the IBM classical
devices show that our circuits succeed at simulating the system. However, duo
to scattered results, we execute only the iterative phase estimation part of
the circuit on the 5 qubit quantum devices to reduce the circuit size and
obtain low-scattered results.
