To get true answers from this complex math, physicists multiply the wave function by the negative version of itself. The result is the probability of observing an object with the properties specified in the wave function. Summing up all the squares of all solutions for any quantum object always gives 100%. The Schrödinger equation takes every possibility into account. This is confusing but not surprising.
The fundamental instrument of quantum mechanics, of which all its singularities are composed, is the wave function. Every possible state of a quantum object, every possible measurement result is a solution of the Schrödinger equation. This simple equation is similar to the one that describes moving waves - enough to confuse Erwin Schrödinger with calling his solutions wave functions - but quantum waves are abstract, not real. Unlike ocean or sound breakwaters, wave functions always contain imaginary numbers.