June, 2005

Abstract

The notion of the quantum angle is introduced.
The quantum angle turns out to be a metric on the set of
physical states of a quantum system.
Its kinematics and dynamics are studied.
The *certainty* principle
for quantum systems is formulated and proved.
It turns out that the certainty principle
is closely connected with the Heisenberg uncertainty principle
(it presents, in some sense, an opposite point of view).
But at the same time the certainty principle allows to give
rigorous formulations for wider class of problems
(it allows to rigorously interpret and ground the analogous
inequalities for the pairs of quantities like
time - energy, angle - angular momentum etc.).

Note: |

This original paper is given here for people interested in the history of the certainty principle. People, who just want to get acquainted with a scientific view of the question, should read The certainty principle (review), where a more systematic explanation is given. |

Proof of the uncertainty principle

March, 2006

Abstract

A more detailed derivation of the Heisenberg uncertainty principle from
the certainty principle is given.

Note: |

This original paper is given here for people interested in the history of the certainty principle. People, who just want to get acquainted with a scientific view of the question, should read The certainty principle (review), where a more systematic explanation is given. |