The development of quantum theory was indeed driven by a combination of experimental observations and mathematical formulations. Physicists at the turn of the 20th century encountered a series of experimental results that could not be explained by classical physics, leading to a need for a new theoretical framework.
Scientists, including Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, and others, made significant contributions to the development of quantum theory. They worked to reconcile experimental observations, such as the blackbody radiation spectrum and the photoelectric effect, with theoretical models.
One of the key milestones in the development of quantum theory was Max Planck's proposal in 1900 that energy is quantized into discrete packets called "quanta." Planck introduced this concept to explain the observed spectrum of radiation emitted by a blackbody, which classical theories failed to account for. This idea laid the foundation for the birth of quantum mechanics.
Albert Einstein further advanced the understanding of the quantum nature of light with his work on the photoelectric effect in 1905. He postulated that light consists of discrete packets of energy called photons, which could explain the experimental results.
The development of quantum theory also involved the mathematical formulations and formalisms developed by physicists. Werner Heisenberg, Max Born, and Pascual Jordan, for example, introduced matrix mechanics in 1925 as a mathematical framework for quantum mechanics. At the same time, Erwin Schrödinger developed wave mechanics, which described particles as wave-like entities represented by wave functions.
These mathematical formulations were inspired by experimental observations, but they also guided further experimental investigations. Scientists worked to refine and verify the predictions of quantum theory through experiments and compared the results with the mathematical formalisms. This iterative process of experimentation and theoretical development led to the establishment of quantum theory as a consistent and accurate description of the microscopic world.
In summary, physicists did indeed strive to find mathematical formulations that matched experimental results while developing quantum theory. The experimental observations posed challenges to classical physics, and the quest for explanations led to the formulation of new mathematical frameworks and theories that eventually became quantum mechanics.