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:
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (1890–1960)
“Such condition of suspended judgment indeed, in its more genial development and under felicitous culture, is but the expectation, the receptivity, of the faithful scholar, determined not to foreclose what is still a question—the “philosophic temper,” in short, for which a survival of query will be still the salt of truth, even in the most absolutely ascertained knowledge.”
—Walter Pater (1839–1894)