Mathematical Development
Once Heisenberg introduced the matrices for X and P, he could find their matrix elements in special cases by guesswork, guided by the correspondence principle. Since the matrix elements are the quantum mechanical analogs of Fourier coefficients of the classical orbits, the simplest case is the harmonic oscillator, where X(t) and P(t) are sinusoidal.
Read more about this topic: Matrix Mechanics
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“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“The work of adult life is not easy. As in childhood, each step presents not only new tasks of development but requires a letting go of the techniques that worked before. With each passage some magic must be given up, some cherished illusion of safety and comfortably familiar sense of self must be cast off, to allow for the greater expansion of our distinctiveness.”
—Gail Sheehy (20th century)