Is supersaturation possible if recrystallization occurs as a solution of a solid in water cools?

Supersaturation is possible

Explanation:

As a solution of solid in water cools, the dissolved solid would begin to reappear as the solution is now supersaturated at that lower temperature.

When the temperature of a solution is increased, more solute are able to dissolve in solution. A supersaturated solution is one that contains more than the required amount of solute needed to saturate the solution at that particular temperature.

Technically, "quantum theory" is actually just the theory associated with quantum mechanics, ie; the theory of any objects isolated from their surroundings but, because it is very difficult to isolate large objects from their environments, it essentially becomes a theory of the microscopic world of atoms and sub-atomic particles.