Introduction
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.
The postulates of quantum mechanics
| Classical mechanics | Quantum mechanics |
|---|---|
| A physical system is represented by a point on the phase space. |
A physical system is represented by a vector (state vector), an element of complex hilbert space. |
| The measurement of the physical quantity is expressed as a function of coordinates of phase space. |
The measurement of the physical value is expressed as a hermetian operator, and the measurement value can only be an eigenvalue of the operator. |
| The measurement of physical quantity has no effect on the system. |
The probability of eigenvalue $q$ as a measure of observable $Q$ is proportional to $\vert⟨q\vert\psi⟩\vert^2$. As a result of the measurement, the state vector changes from $\ket{\psi}$ to $\ket{q}$. |
| A physical system follows Hamilton’s equation of motion. | A physical system follows Schrödinger equation. |