Erwin Schrödinger didn't actually come up with an "atomic theory" in the same way that Dalton or Bohr did. He formulated the Schrödinger equation, a fundamental equation in quantum mechanics that describes the behavior of atomic and subatomic particles. This equation is central to understanding the quantum world, and it's a far cry from the simpler models of the atom that came before it.

Here's how Schrödinger developed his equation:

1. Building on Existing Ideas: Schrödinger was aware of the limitations of Bohr's atomic model, which could only explain the behavior of hydrogen. He also knew of the wave-particle duality of light, proposed by de Broglie, which suggested that particles could also exhibit wave-like properties.

2. The Wave Equation: Drawing inspiration from these concepts, Schrödinger set out to develop a mathematical description of an electron in an atom as a wave. He adapted the wave equation from classical physics to describe the wave function of an electron. This wave function contains information about the probability of finding the electron at a given location and time.

3. The Schrödinger Equation: The resulting equation, known as the Schrödinger equation, is a complex mathematical expression that governs the behavior of the wave function. It describes how the wave function of an electron changes over time under the influence of the atomic nucleus and other forces.

4. Solving the Equation: Solving the Schrödinger equation for a given atom yields a set of solutions called wave functions. Each wave function corresponds to a specific energy level and orbital shape for an electron within the atom. These solutions provide the basis for understanding the electronic structure of atoms and molecules.

Key Points:

* The Schrödinger equation doesn't describe the atom as a miniature solar system with electrons orbiting the nucleus like planets. Instead, it describes the electrons as probability waves, spread out in space around the nucleus.

* The Schrödinger equation revolutionized our understanding of the atom, laying the foundation for modern quantum chemistry and our ability to predict and understand the properties of atoms and molecules.

In conclusion, Schrödinger didn't propose a new atomic theory in the traditional sense. He developed a mathematical framework – the Schrödinger equation – that allows us to accurately describe the behavior of electrons in atoms and molecules. This equation marked a paradigm shift in our understanding of the atom, moving away from classical physics and into the realm of quantum mechanics.