Final answer:
The statement is true; the Schrödinger equation can be precisely solved for the hydrogen atom due to its single electron structure. This exact solution is unique to hydrogen and does not apply to multi-electron atoms, which require complex approximations.
Step-by-step explanation:
The statement "Hydrogen is the only atom for which the Schrödinger equation has an exact solution." is True. The Schrödinger equation is fully solvable only for the hydrogen atom, which consists of a single electron orbiting a proton nucleus. In contrast, multi-electron atoms require approximations because the interaction between multiple electrons introduces complexities that preclude an exact solution.
The hydrogen atom is unique because it's the simplest atom, which allows for a precise mathematical solution to the Schrödinger equation. The success of the Schrödinger model lies in its ability to provide probability statements for an electron's position and energy levels based on its quantum numbers (n, l, m), where 'n' is the principal quantum number, 'l' is the azimuthal quantum number, and 'm' is the magnetic quantum number. These quantum numbers pattern after Bohr's model of the atom, which depicted electrons in fixed orbits but lacked the probabilistic nature of quantum mechanics.