An Invitation to Quantum Mathematics

Quantum Mathematics is the mathematical apparatus of quantum mechanics.


What is the essence of this mathematical ideology ?

We can say quantum mathematics emerges from the classical mathematics
after replacing functions by operators. The outstanding role of
functions in classical mathematics with the pointwise commutative
multiplication is passed in quantum mathematics to operators with their
non-commutative multiplication (composition).

The following 2 statements serve as a "guide to action":
* Classical Mathematics deals exclusively with spaces of functions and
its main structure is the uniform norm.
* Quantum Mathematics deals with the spaces of operators and the main
structure is the quantum norm.

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