We address four physics opportunities. First, predict new elementary particles and forces. Second, explain phenomena such as dark matter. Third, unite physics theories and models. Fourth, point to opportunities for further research. We use models based on solutions to equations featuring isotropic pairs of isotropic quantum harmonic oscillators. First, we show solutions that match the known elementary particles. We propose that other solutions correlate with elementary particles that people have yet to detect and with dark energy forces leading to the three known eras - initial acceleration, subsequent deceleration, and current acceleration - pertaining to the rate of expansion of the universe. Second, we extend solutions to encompass known conservation-law symmetries. We note that extended solutions correlate with known kinematics. We propose that extended solutions describe dark matter, explain ratios of density of dark matter to density of ordinary matter, correlate with dark energy density, and explain other phenomena. Third, we note that the work unites, extends, and limits aspects of traditional physics. Those aspects include classical physics, special relativity, general relativity, quantum mechanics, the elementary particle Standard Model, and the cosmology timeline. The work provides possible insight regarding foundations of physics topics. Fourth, we suggest opportunities for people. We suggest opportunities for observational, experimental, and theoretical physics research. We point to possible opportunities to further develop and apply math we use.