Question

Quantum mechanics for macroscopic charges?

Answer 1

Quantum mechanics will tell us what happens in such a system, and indeed by solving the Schrodinger equation... ☺ ☺

Answer 2

There are certain physical phenomena that need quantum mechanics even at the macroscopic level,like the Bose-Einstein condensation and superconductivity.And even in normal macroscopic situations its not that quantum theory is not applicable but it becomes irrelevant at macroscopic level. Like you can always explain the classical gas thermodynamic behavior by using quantum statistics but its easy to use classical statistics.

What exactly happens in most of the cases is that if you are using the quantum theory to explain certain situation then your results actually reduce to your classical results under the your classical limits(high temperature,low density).For example the harmonic oscillator case,the quantum probability of locating the particle starts tending towards the classical probability in high energy limits.

According to the correspondence principle,every quantum theory should result into classical results in the limit of large quantum numbers.