Re: An Invitation to Quantum Mathematics


Mpilot wrote:
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.

Will you please discuss Jx, Jy, and Jz ?

-Tim

.

Relevant Pages

  • An Invitation to Quantum Mathematics
    ... Quantum Mathematics is the mathematical apparatus of quantum mechanics. ... We can say quantum mathematics emerges from the classical mathematics ... its main structure is the uniform norm. ...
    (sci.math)
  • Re: Existence of reals and observation of them
    ... theory and real analysis in university, ... written by people with degrees in mathematics. ... mathematics that is steeped in classical mathematics raises all kinds ... but rather of understanding what a proof from axioms IS and the sense ...
    (sci.math)
  • Classical mathematics is false-impredicative definitions
    ... Classical mathematics is false. ... upon and uses impredicative definitions i.e axiomatic theory. ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... > An expert in constructivism once said to me that there ... > seemed to be areas in classical mathematics that had no real ... > When the axiom of choice isn't used, ...
    (sci.math)