Heisenberg Matrix Quantum Mechanics The Harmonic Oscillator

6 HEISENBERG MATRIX QUANTUM MECHANICS THE HARMONIC OSCILLATOR 

Recognizing the fact that representation of observable quantum operators, in various bases, is made by (hermitic) matrices, Heisenberg had generalized the commutation rules to operators and thus to matrix level, while this way constructing the so-called quantum matrix mechanics. It is basically founded by the commutation rules among the coordinate [2] momentum [- ] matrices. 

the internal consistency of the matrix approach is based on the important Lemma according which the relationships that hold between 

Quantum Nanochemistry-Volume I Quantum Theory and Observability 

The true of this fact may be efficiently exemplified in the case of summation and multiplication operations  

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