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)
“I have an intense personal interest in making the use of American capital in the development of China an instrument for the promotion of the welfare of China, and an increase in her material prosperity without entanglements or creating embarrassment affecting the growth of her independent political power, and the preservation of her territorial integrity.”
—William Howard Taft (1857–1930)