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Simple statement of the postulates of quantum mechanics

Below, we summarize the basic postulates of quantum mechanics and contrast them with roughly equivalent postulates of classical mechanics.



Classical:

1.
Particles are point-like objects that follow predictable, deterministic paths with well-defined positions and momenta obtained by solving Newton's laws of motion

2.
The energy of a system can take on any value.

3.
If the initial conditions of an experiment repeated many times are the same in each repetition, the outcome of the experiment will be the same for each repetition, and that outcome is predictable.

Quantum:

1.
Particles can exhibit wave-like or particle-like behavior, depending on the experiment. Even within the particle-like interpretation, particles do not follow well-defined, predictable paths and hence, do not have well-defined positions and momenta.

2.
The energy can take on only certain discrete values.

3.
Even if a system is prepared in the same way for different repetitions of an experiment, the outcome need not be the same in each repetition. All that we can predict is the probability that a given outcome will be obtained.


next up previous
Next: Heisenberg's uncertainty principle Up: lecture_5 Previous: Sum over paths picture
Mark E. Tuckerman 2011-12-12