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)
“Ultimately, it is the receiving of the child and hearing what he or she has to say that develops the child’s mind and personhood.... Parents who enter into a dialogue with their children, who draw out and respect their opinions, are more likely to have children whose intellectual and ethical development proceeds rapidly and surely.”
—Mary Field Belenky (20th century)