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I know what orbitals are. The orbitals are solutions (also called wave functions) to the (time-independent) Schrödinger equation[ref].

What I don't understand is why p,d,f orbitals have non spherical and s has a spherical shape. Our universe is made up of many circular or spherically (not perfect) shaped objects like stars, planets, bubbles, droplets, wheels etc. I always thought (or guessed) circular and spherical shapes are the most efficient shapes in our universe. Then why p,d and f have non-spherical shapes or non efficient? Is there any other logic other than solution to Schrodinger equation which explains these unique shapes?


marked as duplicate by jerepierre, Todd Minehardt, hBy2Py, M.A.R., Jon Custer Mar 17 '16 at 20:17

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