  Starting from a time-dependent Schr\"odinger equation, stationary states of
3D central potentials are obtained. An imaginary-time evolution technique
coupled with the minimization of energy expectation value, subject to the
orthogonality constraint leads to ground and excited states. The desired
diffusion equation is solved by means of a finite-difference approach to
produce accurate wave functions, energies, probability densities and other
expectation values. Applications in case of 3D isotropic harmonic oscillator,
Morse as well the spiked harmonic oscillator are made. Comparison with
literature data reveals that this is able to produce high-quality and
competitive results. The method could be useful for this and other similar
potentials of interest in quantum mechanics. Future and outlook of the method
is briefly discussed.
