  We have proposed and validated an ansatz as effective potential for confining
electron/hole within spherical quantum dot in order to understand quantum
confinement and its consequences associated with energy states and band gap of
Spherical Quantum Dot. Within effective mass approximation formalism,
considering an ansatz incorporating a conjoined harmonic oscillator and coulomb
interaction as the effective potential for confining an electron or a hole
within a spherical quantum dot and by employing appropriate boundary conditions
we have calculated the shifts in energy of minimum of conduction band(CBM) and
maximum of valence band(VBM) with respect to size of spherical quantum dot. We
have also determined the quantum confinement induced shift in band gap energy
of spherical quantum dot. In order to verify our theoretical predictions as
well as to validate our ansatz, we have performed phenomenological analysis in
comparison with available experimental results for quantum dots made of CdSe
and observe a very good agreement in this regard. Our experimentally consistent
theoretical results also help in mapping the probability density of electron
and hole inside spherical quantum dot. The consistency of our results with
available experimental data signifies the capability as well as applicability
of the ansatz for the effective confining potential to have reasonable
information in the study of real nano-structured spherical systems.
