you could only work with probability and mathematical formulations. (Heisenberg called this matrix mechanics, soon shown to be equivalent to Erwin Schrödinger's more visualizable wave theory.) ...

Werner Heisenberg's high school years were interrupted ... To do this he applied a mathematical system to atomic physics, called matrix mechanics. It was a turning point for physics.

This module builds on the quantum mechanics learned in the perquisites PHY250 and PHY251. The Heisenberg matrix formulation of the theory is developed from the Schrodinger wave picture. Approximately ...

Heisenberg, Max Born and Pascual Jordan — Paul Dirac made independent contributions — expanded the approach into what would become known as the matrix-mechanics formulation of quantum mechanics.