It is a rather disheartening experience to be told that the exact solution of the wave equation will in the end be the solution of the wave equation of one single atom, and that for an aggregate of atoms, the exact solution is out of reach.
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"Consciousness is a singular of which the plural is unknown; that there is only one thing and that what seems to be a plurality is merely a series of different aspects of this one thing."
"The unity and continuity of Vedanta are reflected in the unity and continuity of wave mechanics. This is a brilliant insight."
"The number of children born from educated parents is much too small."
"The true path to knowledge is to question everything."
"The existence of life on Earth is just a fluke. There is no special reason for it."
Austrian physicist who shared the 1933 Nobel for the wave equation that bears his name and the famous cat thought-experiment. Closely associated with Werner Heisenberg (matrix-mechanics rival who reached the same physics by different math) and Albert Einstein (his pen-pal on quantum interpretation). For an intellectual contrast, see Niels Bohr, Danish physicist and architect of the Copenhagen interpretation — Schrödinger's cat thought-experiment was specifically designed to ridicule Bohr's 'observer-dependent reality' reading of quantum mechanics — Schrödinger thought the Copenhagen interpretation was absurd; the cat was meant as reductio ad absurdum.
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Quantum mechanics, despite its revolutionary equations, hits a hard wall with complexity. Schrödinger's wave equation can be solved exactly only for a single isolated atom — hydrogen being the prime example. For any system with multiple atoms, the math explodes into analytically unsolvable territory. Scientists must rely on approximations rather than exact answers. This exposes a sobering gap between elegant theory and physical reality: the universe's complexity fundamentally outpaces our analytical tools.
Schrödinger derived his famous wave equation in 1926, personally solving it exactly for hydrogen — a landmark achievement. Yet he understood intimately that his own equation became analytically intractable beyond that single-electron case. He later explored biology's complexity in "What is Life?" (1944), showing sustained concern with how physical laws handle complex systems. This quote reflects his characteristic intellectual honesty: celebrating theory while unflinchingly acknowledging where it breaks down in practice.
By the late 1920s, quantum mechanics was revolutionary but immediately confronted the many-body problem. Exact solutions existed only for hydrogen; even helium resisted exact treatment. This drove rapid development of approximation methods — perturbation theory, Hartree-Fock, variational approaches — throughout the 1930s. Simultaneously, the Great Depression reshaped academic funding and rising nationalism fragmented European scientific communities, pressuring physicists to produce practical results while wrestling with the internal mathematical limits of their own framework.
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