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When the electron became a wave, the Schrdinger bohrer and the music inside the atom.
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Welcome back to Quantum on the Treadmill, where I use my time on the treadmill to explore the people, ideas, and strange turns that created quantum mechanics.
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In our journey so far, we have seen physicists slowly dismantle the comfortable mechanical universe inherited from Newton.
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Planck discovered that energy seemed to come in discrete packets.
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Einstein proposed that light itself could behave as particles.
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Bohr then placed those ideas inside the atom, arguing that electrons could occupy only certain energy levels and could jump from one level to another.
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Bohr's model worked surprisingly well, but it left behind an enormous unanswered question.
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Why?
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Why could an electron occupy one energy level but not the space between levels?
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Why were only certain orbits permitted?
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And what exactly happened when an electron performed one of Bohr's mysterious quantum jumps?
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Bohr had discovered an astonishing rule about nature, but he had not really explained where the rule came from.
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Then Erwin Schrödinger entered the story and proposed something even stranger.
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What if the electron was not best understood as a tiny object traveling around the nucleus?
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What if it had to be understood as a wave?
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The problem with Bohr's atom.
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Bohr's atom is easy to picture.
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It resembles a miniature solar system.
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The nucleus sits in the center like the sun, while electrons travel around it in permitted orbits.
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But Bohr's orbits were not ordinary orbits.
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A planet can circle the Sun at many different distances, move it slightly closer or farther away, and it simply settles into a different orbit.
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Bohr said electrons could not do that.
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They could exist only at particular energy levels.
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An electron could occupy one level or another, but it could not settle halfway between them.
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When an electron moved from a higher energy level to a lower one, the atom released the difference as a specific packet of light.
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That helped explain why atoms produced distinctive lines of color rather than a continuous rainbow, but Bohr had essentially declared that only certain orbits were allowed.
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His model did not explain
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why nature selected those particular orbits.
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It is also worth clearing up a common confusion.
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Bohr's model was about electrons orbiting the nucleus.
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It was not about electron spin.
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Spin is a separate quantum property that entered the story later.
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Although we use the word spin, an electron is not simply a tiny ball rotating like Earth.
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Bohr was still trying to preserve part of the old mechanical picture.
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The electron remained a particle traveling along an orbit.
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Schrödinger would eventually replace that picture with something much less familiar.
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A wave before Schrdinger.
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The idea did not begin entirely with Schrdinger.
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A few years earlier a young French physicist named Louis de Broly had noticed a strange imbalance in quantum physics.
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Einstein had shown that light, which had long been understood as a wave, could also behave like a collection of particles.
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De Broly asked a wonderfully simple question.
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If a wave can behave like a particle, could a particle behave like a wave?
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He proposed that material objects, including electrons, have a wavelength associated with them.
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An electron with greater momentum would have a shorter wavelength.
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An electron with less momentum would have a longer wavelength, and this sounded radical, but it gave Schrödinger a clue about Bohr's permitted orbits.
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Imagine a wave traveling around a circle.
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After completing one trip, the wave has to meet itself again.
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If the crest of the returning wave meets another crest and the trough meets another trough, the wave reinforces itself.
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It creates a stable pattern.
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But if a crest returns and meets a trough, the wave begins to cancel itself out.
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That pattern cannot remain stable.
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This is similar to what happens on a guitar string.
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A string cannot produce just any stable vibration.
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The wave must fit the length of the string.
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Some patterns fit perfectly and produce clear notes.
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Other patterns interfere with themselves and quickly disappear.
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Schrdinger began to see the electron around the nucleus in a similar way.
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Perhaps Bohr's permitted energies existed because only certain electron waves could form stable patterns.
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The forbidden spaces between Bohr's levels were not being prohibited by an arbitrary rule.
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They were patterns that simply could not fit.
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Bohr had identified the permitted notes.
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Schrdinger was beginning to discover the instrument.
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What did Schrdinger mean by a wave?
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When we hear the word wave, we usually imagine water rising and falling, a sound moving through the air, or a guitar string vibrating back and forth.
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In each case, something appears to be waving.
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Water waves involve moving water, sound waves involve changing pressure in the air.
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A guitar string physically changes position.
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So what was waving in Schrdinger's theory?
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That became one of the deepest questions in quantum mechanics.
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Schrdinger initially hoped that an electron might literally be a physical wave, perhaps a distribution of electrical charge spread through space.
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But this interpretation created problems.
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When physicists detect an electron, they do not normally find fragments of it scattered throughout the laboratory.
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They detect a complete electron in a particular place.
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The physicist Max Born offered the interpretation that eventually became standard.
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Schrödinger's wave does not describe a material substance spread through space in the ordinary sense.
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It describes the possibilities for what we might observe.
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The wave is represented by something called the wave function.
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The wave function contains information about the electron's quantum state.
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When physicists mathematically square its magnitude, they obtain the probability of detecting the electron in different places.
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Where the wave function is strong, the electron is more likely to be detected.
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Where it is weak, the electron is less likely to be detected.
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Where it falls to zero, the electron will not be detected.
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This is not merely a statement that the electron occupies a definite position, and we happen not to know where it is.
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Before measurement, quantum mechanics describes the electron through a spread of possible outcomes.
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That is one of the most difficult shifts in the quantum story.
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The wave is not necessarily a wave of physical stuff, it is a structured wave of possibility.
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How Schrodinger found his equation.
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Schrodinger now needed more than an interesting picture.
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He needed an equation that could describe how these matter waves behaved.
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He drew together several different clues.
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The first was de Broly's connection between a particle's motion and its wavelength.
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The second came from the traditional mathematics of waves.
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Physicists already had equations describing how waves change through space and time.
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The third clue came from classical mechanics, particularly the work of the 19th-century mathematician William Rowan Hamilton.
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Hamilton had developed an elegant way to describe the motion and energy of physical systems.
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Schrdinger noticed that parts of Hamilton's mechanics looked remarkably similar to the mathematics used to describe the movement of waves and light.
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This suggested that classical particles might be only part of a larger picture.
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A ray of light looks as though it follows a precise path, but underneath that path is a spreading electromagnetic wave.
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Perhaps the paths of classical particles were also approximations of some deeper wave behavior.
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Schrdinger looked for an equation that combined the electron's total energy, its motion, the forces acting upon it, and its wave-like nature.
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In plain language, the equation asks something like this: given the energy of a quantum system and the forces acting within it, what wave patterns are possible and how will those patterns change over time?
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For an electron bound to a nucleus, Schrdinger searched for stable wave patterns.
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He effectively treated the atom like a three-dimensional musical instrument and asked which notes it could play.
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When he solved the equation for hydrogen, something extraordinary happened.
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Only particular solutions worked.
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Each acceptable wave pattern came with a particular energy.
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Those energies matched the levels Bohr had already proposed and the spectral lines scientists had observed in experiments.
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But Schrdinger had not placed Bohr's energy levels into the theory as special rules.
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The energy levels emerged naturally from the equation.
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That was the breakthrough.
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Bohr said the electron was permitted to occupy only certain energies.
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Schrdinger showed that only certain wave patterns could exist as stable states from orbits to orbitals.
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Schrödinger's work also changed the picture of the atom.
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In Bohr's model, electrons traveled along defined orbits.
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In Schrdinger's quantum mechanics, electrons occupied orbitals.
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The words sound similar, but they describe very different ideas.
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An orbit is a path.
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An orbital is a three-dimensional probability pattern produced by the wave function.
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The simplest orbital around a nucleus is spherical.
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Other orbitals form shapes that resemble dumbbells, rings, or more complicated arrangements of lobes.
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These shapes do not represent solid containers holding the electron.
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They show where the electron is more or less likely to be detected.
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The shapes arise for the same basic reason that different musical notes have different vibration patterns.
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They are the permitted standing waves of the atom.
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This also helps explain why electrons do not simply fall into the nucleus.
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An electron in an atom is not a tiny planet gradually losing energy and spiraling inward.
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It occupies a stable quantum state.
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The lowest energy state is the lowest permitted note of the atomic instrument.
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There is no lower stable wave pattern into which it can continuously collapse.
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That's why Schrodinger's equation matters.
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Schrodinger's equation became one of the foundations of modern physics because it did far more than improve Bohr's model of hydrogen.
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It helped explain the structure of more complicated atoms.
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Those atomic structures helped explain chemical bonds, the organization of the periodic table, and why different elements behave differently.
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Chemistry became understandable at a deeper level because the ways atoms combine are largely determined by the quantum states of their electrons.
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The same framework eventually helped us understand solids, semiconductors, lasers, superconductors, molecular biology, and much of modern material science.
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The computers and phones we use today depend on technologies built from our ability to understand and manipulate electron states.
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Schrdinger's equation plays a role in quantum mechanics similar to the role Newton's laws play in classical mechanics.
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If we know the initial quantum state and the forces acting on the system, the equation tells us how the wave function develops over time, but it comes with an important mystery.
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The Schrdinger equation describes the wave function changing smoothly and predictably.
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Measurement, however, gives us one definite outcome.
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We do not observe a blurred mixture of possible electron locations.
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We detect the electron in one place, and the equation tells us how the field of possibilities evolves, but it does not by itself completely explain why one particular possibility becomes the result we experience.
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That gap would produce some of the greatest arguments in twentieth century physics, including debates between Einstein and Bohr and Schrdinger's own famous story about a cat that appears to be both alive and dead.
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The bigger shifts.
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The real importance of Schrdinger's work was not merely that he found a better way to calculate atomic energies.
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He changed what physicists thought a physical explanation could look like.
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Bohr still gave us something resembling a mechanical model.
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There was a nucleus, an electron, and a collection of permitted orbits.
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Schrdinger replaced those orbits with mathematical waves of possibility.
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The electron did not simply have a hidden path waiting for us to discover it.
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Its quantum state was spread across a range of possible observations.
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The stable structures inside the atom were not miniature planetary systems, they were standing wave patterns.
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This is the transition I find most helpful.
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Bohr discovered that the atom played only certain notes.
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De Broly suggested that matter itself might have a wavelength.
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Schrdinger built the equation that revealed the instrument and explained why only those notes were possible.
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Born then told us that the music was not describing where the electron definitely was, it was describing where the electron might be found.
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Schrdinger therefore solved one mystery while opening another.
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He showed how the strange jumps in Bohr's atom could emerge from stable waves.
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But he also forced physics to confront a more unsettling question.
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If the quantum wave describes many possibilities, how does the world we observe end up giving us only one reality?
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And that is where our walk through quantum history becomes even stranger.