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Starting from a time-dependent Schr\"odinger equation, stationary states of3D central potentials are obtained. An imaginary-time evolution techniquecoupled with the minimization of energy expectation value, subject to theorthogonality constraint leads to ground and excited states. The desireddiffusion equation is solved by means of a finite-difference approach toproduce accurate wave functions, energies, probability densities and otherexpectation values. Applications in case of 3D isotropic harmonic oscillator,Morse as well the spiked harmonic oscillator are made. Comparison withliterature data reveals that this is able to produce high-quality andcompetitive results. The method could be useful for this and other similarpotentials of interest in quantum mechanics. Future and outlook of the methodis briefly discussed.

Ground and excited states of spherically symmetric potentials through an imaginary-time evolution method: Application to spiked harmonic oscillators