A tale of two representations: energy and time in photoabsorption

This essay is based on a talk at Advances in Atomic, Molecular, and Optical Sciences 2020 (AAMOS20) symposium honoring Prof. S. T. Manson's decades-long contribution to photoabsorption studies. Quantum physics introduced into pairs of conjugate quantities bearing specific complementary relationship, energy time being one such pair. gives rise two alternative representations, time-dependent time-independent one, seemingly very different but both capable embracing the same physics. They give descriptions insight, with technical questions, theoretical experimental, determining which may be more convenient practicable any juncture. Two recent topics, Cooper minima Cl$^-$ Ar, angular-momentum barrier tunneling $f$ photoelectrons from Se WSe$_2$, provide illustrative examples, also role that technological developments over past five decades played our approach understanding phenomena.