The fundamental equation of quantum mechanics whose solutions give electron wave functions and allowed energies.
Practise Atomic Structure & Periodicity All Atomic Structure & Periodicity topics
The Schrodinger equation, H psi = E psi, is the fundamental equation of quantum mechanics, where H is the Hamiltonian operator and E is the energy. Solutions exist only for certain energies when suitable boundary conditions are applied, and these discrete solutions naturally give the quantum numbers. It was published by Erwin Schrodinger in 1926. It can be solved exactly for the hydrogen atom, giving the same energy levels as Bohr together with the orbital shapes. Many-electron atoms require approximation methods such as Hartree-Fock.
Key ideas: H psi = E psi, where H is the Hamiltonian (kinetic plus potential operator). For hydrogen, solutions exist only for certain E values, which are -13.6 eV / n^2, matching Bohr, and quantum numbers n, l, ml arise naturally from boundary conditions. It cannot be solved exactly for more than one electron, so approximations are used.
Common mistakes and connections: Students think it can be solved exactly for helium; it cannot, and methods like Hartree-Fock and DFT are used. Another is thinking the equation shows electron paths, whereas it yields only probabilities. Its solutions are atomic orbitals, building the foundation for electron configuration and bonding theory.
Solving the Schrodinger equation for a confined particle gives quantized energy proportional to n squared and wave functions with n-1 nodes. The interactive lesson shows this as a live animation or chart.
Solving it for hydrogen gives energy levels matching the Bohr results, plus orbital shapes such as the 2p dumbbell.
The fundamental equation of quantum mechanics whose solutions give electron wave functions and allowed energies.
Schrodinger Equation is a advanced topic in Atomic Structure & Periodicity. It builds on beginner and intermediate topics, so review those first if needed.
Study these earlier topics in Atomic Structure & Periodicity first: de Broglie Hypothesis, Heisenberg Uncertainty Principle, Wave Function.
The next topics in Atomic Structure & Periodicity are Atomic Orbital and Principal Quantum Number.
Yes. The interactive lesson includes a self-check question on Schrodinger Equation, and the Atomic Structure & Periodicity quiz draws on every topic in this area.
Schrodinger Equation is topic 51 of 115 in Atomic Structure & Periodicity.