Schrödinger equation
The basic equation of quantum mechanics, which governs how the wave of an electron or other particle varies in space and time. Written down by Erwin Schrödinger in 1926.
Early in 1926 Erwin Schrödinger at the University of Zurich took de Broglie's matter waves as his clue and published the equation an electron's wave obeys[1]. Just as a plucked string can sound only certain notes, the wave of an electron held by a nucleus can vibrate only in certain patterns. Calculating the energy of each pattern reproduced the sequence of hydrogen energies Bohr had found in 1913, without any rules added after the fact.
The same year Schrödinger himself showed that it was the same theory, underneath, as the matrix mechanics of Heisenberg and his colleagues[2]. As for what the wave (the wave function) represents, Max Born proposed that it sets the probability of finding the electron at each place, and that reading became standard.
The behaviour of electrons in atoms, molecules and semiconductors is still studied by solving this equation. As the number of electrons grows, however, the amount of calculation balloons, and it can be solved exactly only in simple cases such as the hydrogen atom.
Related terms
- Matter waveThe idea that things long taken to be particles, such as electrons, also behave as waves. Proposed by Louis de Broglie in 1924.
- Matrix mechanicsThe first form of quantum mechanics, born in 1925: it describes electrons in atoms using only observable quantities, calculated as tables of numbers called matrices.
- Uncertainty relationThe quantum relation that a particle's position and momentum cannot both be pinned down as precisely as you like at the same time. Set out by Werner Heisenberg in 1927.