Question

A. Describe specifically two major differences between quantum mechanics and classical mechanics.

B. How does the correspondence principle link quantum mechanics and classical mechanics?

C. Why is it still accurate to use classical mechanics for human size objects? That is, why are our wave like properties not observed?

Answer 1

A) Quantum Mechanics - Describes small-scale systems like atoms and molecules.. which evolve according to Schrodinger's equation.

The dynamical variables are not continuous quantities, they are discretized due to confinement in the system ( Boundary conditions ).

Classical Mechanics - Describes large-scale systems like Cars, pulleys, etc.. which obey Newton's Laws of Motion.

The dynamical variables are continuous real numbers.

B) The correspondence principle states that under a limit of large systems the quantum mechanics averages out to classical mechanics i.e. a system which is described by QM can be equally described by classical mechanics under the limit of large quantum numbers.

Ehrenfest theorem which describes the evolution of expectation values in terms of laws of classical mechanics supports the correspondence principle.

C) For human-size objects, the effects due to quantum mechanics like de-Broglie wavelength are infinitesimal,

  

Therefore, wavelike properties are not observed for large objects.