The existence of the scar is directly implied by the Ehrenfest theorem.

Taking expectation values yields the Ehrenfest theorem featured in the correspondence principle.

It was established above that the Ehrenfest theorems are consequences of the Schrödinger equation.

However, the converse is also true: the Schrödinger equation can be inferred from the Ehrenfest theorems.

A related equation describes the time evolution of the expectation values of observables, it is given by the Ehrenfest theorem.

Whence, the Schrödinger equation was derived from the Ehrenfest theorems by assuming the canonical commutation relation between the coordinate and momentum.

(Note that there is no simple rigorous mathematical limit which fully recovers classical mechanics from quantum mechanics, the Ehrenfest theorem notwithstanding.

As a consequence, , and then due to the relationship between J and R. By the Ehrenfest theorem, it follows that J is conserved.

He made major contributions to quantum physics, including the theory of phase transitions and the Ehrenfest theorem, which states that expectation values of a quantum system follow classical mechanics.

Paul Ehrenfest (January 18, 1880 - September 25, 1933) was an Austrian and Dutch physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem.

The Ehrenfest theorem, named after Paul Ehrenfest, the Austrian physicist and mathematician, relates the time derivative of the expectation value for a quantum mechanical operator to the expectation of the commutator of that operator with the Hamiltonian of the system, expectations which are connected to classical mechanics.