  We propose a new method to solve the eigen-value problem with a two-center
single-particle potential. This method combines the usual matrix
diagonalization with the method of separable representation of a two-center
potential, that is, an expansion of the two-center potential with a finite
basis set. To this end, we expand the potential on a harmonic oscillator basis,
while single-particle wave functions on a combined basis with a harmonic
oscillator and eigen-functions of a one-dimensional two-center potential. In
order to demonstrate its efficiency, we apply this method to a system with two
$^{16}$O nuclei, in which the potential is given as a sum of two Woods-Saxon
potentials.
