Quantum Mechanics – How Linearity of Quantum Mechanics Differs from Macroscopic Nonlinearity

Question

We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are the physics points of connection between the two descriptions?

Answer 1

There is an all too common misconception that because the Schrodinger equation is linear, non-linear phenomena (like chaos) are only classical. The wavefunction does obey a linear equation, the Schrodinger equation, but it is not directly related to observable physics. Observables quantities, like expectation values of operators, obey non-linear equations. In fact, many times the same equations as their classical counterparts, with small corrections.