In 1929 Paul Dirac pronounced that "the underlying physical laws necessary for the mathematical theory for a large part of physics and the whole of chemistry are...completely known". While the fundamental aspects of non-relativistic quantum mechanics have remained essentially unchanged ever since, physics and chemistry have been driven largely by experiment. Dirac had the answer to that too. To his comment he added a rider: "The difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble."
In 1929 Paul Dirac pronounced that "the underlying physical laws necessary for the mathematical theory for a large part of physics and the whole of chemistry are...completely known". While the fundamental aspects of non-relativistic quantum mechanics have remained essentially unchanged ever since, physics and chemistry have been driven largely by experiment. Dirac had the answer to that too. To his comment he added a rider: "The difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble."
I n the early 20th century, the groundbreaking theories of quantum mechanics and special relativity emerged at roughly the same time.At first, both theories appeared to be entirely incompatible with each other.While the quantum equations written out by Erwin Schrödinger and Wolfgang Pauli dealt with the behaviours of electrons, atoms, and molecules moving at speeds encountered in classical physics, the rules of special relativity first imagined by Albert Einstein described the behaviour of matter moving at close to the speed of light.Initially, this apparent clash of theories presented a crisis in physics.However, in the late 1920s, further theoretical work carried out by physicists including Paul Dirac, Oskar Klein, and Walter Gordon culminated in a new set of equations, which proved definitively that quantum mechanics and special relativity are compatible with each other after all. An educational challengeYet with this groundbreaking discovery came an entirely new problem.In adding a new layer of complexity to the equations of non-relativistic quantum mechanics, the more complete theories of relativistic
Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics? By ‘exact’ I do not of course mean ‘exactly true’. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist...until workable approximations are needed in applications. By ‘serious’ I mean that some substantial fragment of physics should be covered. Nonrelativistic ‘particle’ quantum mechanics, perhaps with the inclusion of the electromagnetic field and cut-off interaction, is serious enough. For it covers ‘a large part of physics and the whole of chemistry’ (P A M Dirac 1929 Proc. R. Soc.A 123 714). I mean too, by ‘serious’, that ‘apparatus’ should not be separated off from the rest of the world into black boxes, as if it were not made of atoms and not ruled by quantum mechanics.
Abstract Chemistry is about the atom and molecule, motion of which follows quantum mechanics established 100 years ago by Werner Heisenberg, inspired by a number of milestone findings including Max Planck’s first quanta concept for black body radiation, Albert Einstein’s photon concept for photoelectric effect and oscillator quanta for heat capacity of solid, and Niels Bohr’s quantum model for atomic structure. Independently, inspired by Louis de Broglie’s particle-wave duality, Erwin Schrödinger established wave mechanics, which is shown to be equivalent to Heisenberg’s mechanics by Paul Dirac. The latter further established the relativistic quantum mechanics, and then claimed that the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws lead to equations much too complicated to be soluble. In the occasion of celebrating The International Year of Quantum Science and Technology (IYQ 2025, quantum2025.org), we will present a heuristic review of the development of quantum theory and its application to chemistry, namely, quantum chemistry (QC). Then, we will discuss some of the current challenges and the future developments, especially on the quantum computing for quantum chemistry (QCQC).
Quantum mechanics is our most successful physical theory. It underlies our very detailed understanding of atomic physics, chemistry, and nuclear physics, and the many technologies to which physical systems in these regimes give rise. Additionally, relativistic quantum mechanics is the basis for the standard model of elementary particles, which very successfully gives a partial unification of the forces operating at the atomic, nuclear, and subnuclear levels. However, from its inception the probabilistic nature of quantum mechanics, and the fact that “quantum measurements” in the orthodox formulation appear to require the intervention of non-quantum mechanical “classical systems,” have led to speculations by many physicists, mathematicians, and philosophers of science that quantum mechanics may be incomplete. Among the Founding Fathers of quantum theory, Einstein and Schrödinger were both of the opinion that quantum mechanics is in some way unsatisfactory, and this view has been amplified in more recent profound work of John Bell, among others. In an opposing camp, many others in the physics, mathematics, and philosophy communities have attempted to provide an interpretational foundation in which quantum mechanics remains a complete and self-contained system. Among the Founding Fathers, Bohr, Born, and Heisenberg maintained that quantum mechanics is a complete system, and a number of recent proposals have been made to improve upon or to provide alternatives to their “Copenhagen Interpretation.” The debate continues, and has spawned an enormous literature.