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When you see pictures of atoms, they are often more accurately described as fuzzy probabilistic clouds.
But, what actually is that cloud mathematically? Is it a ...... vector field? A Lie group? If I wanted to write down a formula that prescribed a "value" or a "probability" to each and every point in 3D space, how would one do that in a manner consistent with the shape you see in atoms?
I'd prefer not to delve into PDE right away, I'd prefer to start with a preliminary example first.
For instance, how would one describe a "fuzzy sphere" in 3D space whose influence decays over distance?
But, what actually is that cloud mathematically? Is it a ...... vector field? A Lie group? If I wanted to write down a formula that prescribed a "value" or a "probability" to each and every point in 3D space, how would one do that in a manner consistent with the shape you see in atoms?
I'd prefer not to delve into PDE right away, I'd prefer to start with a preliminary example first.
For instance, how would one describe a "fuzzy sphere" in 3D space whose influence decays over distance?