Which of the following equations is fundamental to wave mechanics?

Schrödinger's Equation is central to wave mechanics as it governs the behavior of quantum mechanical systems. In wave mechanics, the wave function describes the quantum state of a particle or system, and Schrödinger's Equation is the mathematical formulation that relates the wave function to the energy of the system.

This equation captures the wave-like properties of particles, allowing predictions about behaviors such as interference and diffraction, which are key characteristics of wave mechanics. By solving Schrödinger's Equation, one can understand how quantum states evolve over time and how particles exhibit both particle-like and wave-like behaviors.

In contrast, while Newton's Second Law describes the motion of classical particles and forces, and Maxwell's Equations deal with electromagnetism, they do not specifically address the principles governing quantum waves. The gravity equation, on the other hand, pertains to the force of gravitation and is not involved in wave mechanics. Therefore, Schrödinger's Equation is the fundamental equation when it comes to understanding the dynamics of waves in quantum systems.