Bohr-Schrodinger formalism

Gordon (1968) pointed out that the spectral profile, Eq. 5.3, presents the Bohr-Schrodinger form of spectroscopy, as transitions between stationary Bohr states, represented by time-dependent Schrodinger states, i), /). The Heisenberg form of quantum mechanics gives an equivalent expression that emphasizes the time evolution of the observables rather than that of the states. This formalism leads quite naturally to time-dependent... 

Once the mathematical formalism of theoretical matrix mechanics had been established, all players who contributed to its development, continued their collaboration, under the leadership of Niels Bohr in Copenhagen, to unravel the physical implications of the mathematical theory. This endeavour gained urgent impetus when an independent solution to the mechanics of quantum systems, based on a wave model, was published soon after by Erwin Schrodinger. A real dilemma was created when Schrodinger demonstrated the equivalence of the two approaches when defined as eigenvalue problems, despite the different philosophies which guided the development of the respective theories. The treasured assumption of matrix mechanics that only experimentally measurable observables should feature as variables of the theory clearly disqualified the unobservable wave function, which appears at the heart of wave mechanics. 

The understanding of the quantum mechanics of atoms was pioneered by Bohr, in his theory of the hydrogen atom. This combined the classical ideas on planetary motion—applicable to the atom because of the formal similarity of the gravitational potential to the Coulomb potential between an electron and nucleus—with the quantum ideas that had recently been introduced by Planck and Einstein. This led eventually to the formal theory of quantum mechanics, first discovered by Heisenberg, and most conveniently expressed by Schrodinger in the wave equation that bears his name. 

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