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II Let's Recall and Discuss
Structure of classical and quantum theories
The essential components of classical and quantum theory of a point
particle are compared in the following table.
Quantization of Classical Systems
The quantization of a classical system consists in identifying the commutators
Quantum mechanics of a Point Particle
In classical mechanics the states of a point particle are described by
generalized coordinates and canonical momenta.
When we come to quantum description of a particle, we no longer describe the
states of a point particle by its coordinates and momentum. The dynamical
variables position and momentum become operators. The quantum
states are described by its wave function \(\psi(x,t)\). The wave function
obeys the Schrodinger equation
This is the equation of motion of the quantum particle.
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