Probability densities for the electron of a hydrogen atom in different quantum states. (ref: http://en.wikipedia.org/wiki/Quantum_state)

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Schrodinger Wave Equation. The beauty of it. From the book "Quantum: A Guide for the Perplexed" by Jim Al Khalili

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“The universe seems to like talking to itself faster than the speed of light,” said Steinberg. “I could understand a universe where nothing can go faster than light, but a universe where the internal workings operate faster than light, and yet we’re forbidden from ever making use of that at the macroscopic level — it’s very hard to understand.”

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Wave function - Wikipedia

Elements by Orbital (2003). This representation shows the Pauli exclusion principle, the aufbau principle and Hund's rule in action.

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Does the quantum wave function represent reality? (Phys.org) -- At the heart of quantum mechanics lies the wave function, a probability function used by physicists to understand the nanoscale world. Using the wave function, physicists can calculate a system's future behavior, but only with a certain probability. This inherently probabilistic nature of quantum theory differs from the certainty with which scientists can describe the classical world, leading to a nearly century-long...

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This kaleidoscopic image is a wave function, illustrating the locational probabilities of an excited subatomic particle. The particle is more likely to be in the red areas than in the green; it is least likely to be in the black spaces. Using other particles or magnetic and electric fields, the area can be manipulated into different shapes, in this case, a heartlike shape called a cardioid.

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The First Image Ever of a Hydrogen Atoms Orbital Structure What you’re looking at is the first direct observation of an atom’s electron orbital — an atoms actual wave function! To capture the image, researchers utilized a new quantum microscope — an incredible new device that literally allows scientists to gaze into the quantum realm.

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