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
Famous quotes containing the words mathematical and/or development:
“An accurate charting of the American woman’s progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time—but like a mathematical curve approaching infinity, never touching its goal. . . . Each time, the spiral turns her back just short of the finish line.”
—Susan Faludi (20th century)
“And then ... he flung open the door of my compartment, and ushered in “Ma young and lovely lady!” I muttered to myself with some bitterness. “And this is, of course, the opening scene of Vol. I. She is the Heroine. And I am one of those subordinate characters that only turn up when needed for the development of her destiny, and whose final appearance is outside the church, waiting to greet the Happy Pair!””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)