Just published another blog called The Essential Quantum Mechanics (//http://soi.blogspot.ca/2014/02/the-essential-quantum-mechanics.html). There's a lot of dry stuff - mathematical definitions, theorems, etc. - but if you are patient enough you will find it gratifying in seeing how the Heisenberg Uncertainty Principle arises from that mathematical formalism, one of the greatest accomplishment of the human mind ever.
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Ah yes... I remember being facinated with the Dirac delta function, what a strange beast. My professor went over the same proof and said that mathematicians at the time had a hard time calling it a legitimate function. X)
Quote from: "Manodo"Ah yes... I remember being facinated with the Dirac delta function, what a strange beast. My professor went over the same proof and said that mathematicians at the time had a hard time calling it a legitimate function. X)
Most of those mathematicians are probably dead by now, but they were definitely on the wrong side of history. Anyhow, the delta function was already part of Fourier's integral series (1768 – 1830) , and Cauchy (1789 –1857) had already discovered the exponential form of the delta function. Dirac just put the final touch by identifying it as what was needed to deal with a point mass.
In another forum, someone pointed out that I left out the evolution operator. That would have taken me into the Schroedinger picture Vs the Heisenberg picture. Though that is important, especially when going from QM to QFT, I thought it could be omitted since my goal was to reach the Heisenberg Uncertainty Principle with minimum math development of the theory. But the criticism was legit.
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