Undergrad What inspired Dirac's formulation of quantum theory?

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Dirac's formulation of quantum theory was influenced by Heisenberg's work, particularly the Helgoland article, which left a significant impression on him. He is credited with the first written version of the Heisenberg equation of motion, although he modestly referred to it as such. The discussion highlights the importance of Dirac's approach, emphasizing its clarity and effectiveness for students familiar with Hamiltonian mechanics and Lie algebra. The rarity of Dirac's original texts from the 1920s and 1930s poses a challenge for researchers seeking to understand his inspirations. Overall, Dirac's contributions are regarded as foundational in the field of quantum mechanics.
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"historically the Heinsenberg equation of motion was first written by P. A. M Dirac, who - with his characteristic modesty- called it the Heinsenberg equation of motion."
Modern quantum mechanics/ J.J. Sakurai, page 84

Why dirac did that?, I didn't find any source.

Any information about this will be appreciated
 
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I will check Dirac's articles on QM from 1925 and 1926 to see if this is true. I don't have the 1930 (1st) Edition of his QM treatise, the book is so rare...:(
 
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I think Dirac was inspired to his formulation of quantum theory in terms of what he then called "q-numbers" by reading Heisenberg's famous Helgoland article, which deeply impressed him. Nevertheless, I think Dirac's presentation of QT is the best of all the early papers on the subject. It's the way, I think, QT should be presented from the very beginning. It's easy for students who have heard a good lecture on Hamiltonian mechanics with Poisson brackets and some good portion of Lie-algebra theory coming naturally with it.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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