1933 · Schrödinger & Dirac
Heisenberg's matrix mechanics worked — but hardly anyone could use it. Matrices were alien mathematics to most physicists. Then, in 1926, Erwin Schrödinger found a friendlier road to the same physics. Inspired by de Broglie's matter waves, he asked: what equation does an electron wave obey? Over a Christmas holiday in the Swiss Alps, he wrote down his wave equation — and showed it reproduced all of Bohr's energy levels, naturally, with no ad-hoc rules.
Meanwhile, a quiet 25-year-old at Cambridge, Paul Dirac, was bothered by a deeper problem: Schrödinger's equation ignored relativity. In 1928 Dirac wrote an equation that married quantum mechanics to Einstein's special relativity — and the mathematics calmly predicted something nobody had asked for: for every particle, there must exist an antiparticle with opposite charge. Four years later, Carl Anderson discovered the positron — the electron's antimatter twin — in cosmic rays. Dirac's "unwanted" solutions were real.
Schrödinger and Dirac shared the 1933 Nobel Prize in Physics "for the discovery of new productive forms of atomic theory."
Schrödinger (1926)
Wave mechanics: electrons as waves, evolving smoothly under a wave equation. Intuitive, visual.
Dirac (1928)
Relativistic quantum mechanics: the equation demands antimatter — and the universe agreed.
Go deeper — the math & the rigor
Schrödinger's equation governs how every quantum state evolves in time:
\[i\hbar\,\frac{\partial}{\partial t}|\psi(t)\rangle = \hat{H}\,|\psi(t)\rangle\]
Here \(\hat{H}\) is the Hamiltonian — the operator encoding the system's energy. Solve it, and you know the quantum state at any future time. Dirac's relativistic equation,
\[(i\gamma^\mu\partial_\mu - m)\psi = 0,\]
required four-component wavefunctions — and its negative-energy solutions, reinterpreted, became antimatter. As a bonus, electron spin fell out of Dirac's theory automatically, no longer a hypothesis bolted on by hand.
Why this prize matters for quantum computing: two reasons, both enormous. First, the Schrödinger equation is how qubits evolve: every quantum gate is a brief pulse of some Hamiltonian \(\hat{H}\) applied for a precise time — solving the equation tells you exactly what the gate does. Second, the \(|\psi\rangle\) notation itself was invented by Dirac (his 1939 "bra-ket" notation). Every \(|0\rangle\), \(|1\rangle\), and \(|\Phi^+\rangle\) in this entire course is Dirac's handwriting.
Key takeaways
- Schrödinger's 1926 wave equation describes electrons as waves and reproduces atomic energy levels naturally.
- Dirac's 1928 relativistic equation predicted antimatter; the positron was found in 1932.
- They shared the 1933 Nobel Prize 'for the discovery of new productive forms of atomic theory.'
- Dirac invented bra-ket notation (|ψ⟩) — the language of this entire course.
- Quantum gates are Hamiltonian pulses evolving states via the Schrödinger equation.
Check your understanding
Q1.What did Dirac's relativistic quantum equation predict that nobody had asked for?
Dirac's equation required negative-energy solutions; reinterpreted, they meant every particle has an antiparticle — confirmed by the positron's discovery in 1932.
Q2.Schrödinger and Dirac shared the 1933 Nobel Prize for:
That is the official 1933 motivation — Schrödinger's wave mechanics and Dirac's relativistic theory were new 'forms' of atomic theory.
Q3.Which piece of Dirac's legacy appears on literally every page of quantum computing?
Dirac invented bra-ket notation in 1939; quantum computing's entire language of states and gates is written in it.
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