Kim's most significant contribution was to provide the resolution of the Bohr-Einstein issue of moving hydrogen atoms or moving bound states. Kim was not the first one to recognize the existence of this problem.
Paul Dirac made his life-long efforts to construct the quantum mechanics of bound states (like the hydrogen atom) in Einstein's relativistic world. On this problem, Dirac published four important papers in 1927, 1945, 1949, and 1963. Kim integrated the first three of those four papers using the mathematical formalism provided by
Eugene Wigner. In so doing, Kim provided the resolution to the Bohr-Einstein issue of the moving hydrogen atom, or quantum mechanics of moving bound states in Einstein's relativistic world.
Harmonic Oscillator Wave Functions for moving Bound States In his study regarding quantum mechanics, Kim discussed the role of harmonic oscillators in dealing with bound states. He, together with
Marilyn E. Noz, studied
Murray Gell-Mann’s
quark model, and highlighted that the oscillator wave function can explain the mass spectrum of similar particles observed in high-energy experiments. While following Paul Dirac's papers, he constructed the wave function for the moving
bound state. This wave function is known as the "Lorentz-covariant harmonic oscillator wave function" or "Covariant oscillator wave function." In 1977, Kim and Noz published a paper in the Physical Review discussing that the covariant oscillator wave function can synthesize the quarks and the partons. In 1989, Kim reinforced this result in his paper in
Physical Review Letters. Kim also suggested the possibility to address the Bohr-Einstein issue of moving hydrogen atom with the synthesis of quarks and partons. His studies suggested that this set can also serve as the closed set of commutators for the ten generators for the
Lorentz group applicable to three space coordinates and two time variables if it is possible to contract the second time variables to convert them into four translation generators along the three space coordinates and along the first time variable.
Lorentz Group for Optical Sciences Kim and his co-workers made heavy investments in the Lorentz group. They noted that Dirac's two-oscillator system is directly applicable to two-photons systems in
quantum optics. The two-photon coherent state or the squeezed state of light is a representation of the Lorentz group and shares the same set of mathematical formulas with the Lorentz-covariant harmonic oscillators for moving bound states. Kim and his co-workers also explained how the Lorentz group is applicable to those instruments, including the laser cavities, multilayers, and polarization optics. On this subject, they published a book entitled
Mathematical for Optical Sciences in 2019. ==Awards and honors==