Quantum mechanics is the domain of physics that deals with tiny particles, at the atomic and subatomic scales. At such scales, the behavior of particles is so bizarre that the laws of classical physics no longer remain valid. To explain this queer behavior, variants of equations called Schrödinger Equation are used. Hence, there is discrepancy in the mathematical description of objects and forces at the very large and the very small scales. But recent discovery by Konstantin Batygin, Assistant Professor of Planetary Astrophysics at Caltech, shows that the time dependent Schrödinger Equation might prove helpful in interpreting evolution of certain astronomical structures.

Everything in the universe is in perpetual motion – from relatively small objects such as moons and satellites revolving around planets to huge ones such as stars orbiting the black holes. This kind of motion is governed, according to Einstein, by the curvature of space-time, commonly known as gravity. Gravity also forces these massive objects to form flat, round disks called accreation disks.

An artist’s depiction of accretion disk. Quasi Periodic Oscillations which occur in many accretion disks are an unresolved problem in physics. Source – Wikipedia

Astrophysicists were puzzled by the weird behavior of these astronomical discs. These discs do not retain their circular shape and produce vast amount of distortions in form of ripples and warps. As the emergence of these warps is pretty complex, it was not even possible to model them directly. In pursuit of explaining these astrophysical discs, Batygin used the approximation method known as perturbation theory. This approximation is based upon the equations developed by Lagrange and Laplace. When Batygin used it to approximate evolution of accretion disks by modeling them as series of concentric wires steadily exchanging the orbital angular momentum with one another, he observed the unexpected appearance of the Schrödinger equation.

Back in the 1926, Schrödinger found that the positions of particles are spread out in the whole space, and that only their probabilities could be calculated in the given space. But after a century, Batygin’s research shows that this equation is not just for describing the tiny particles. Bigger objects could also be explained by this quantum equation.

“This discovery is surprising because the Schrödinger Equation is an unlikely formula to arise when looking at distances on the order of light-years. The equations that are relevant to subatomic physics are generally not relevant to massive, astronomical phenomena. Thus, I was fascinated to find a situation in which an equation that is typically used only for very small systems also works in describing very large systems,” Batygin asserts.

“Fundamentally, the Schrödinger Equation governs the evolution of wave-like disturbances,” says Batygin. “In a sense, the waves that represent the warps and lopsidedness of astrophysical disks are not too different from the waves on a vibrating string, which are themselves not too different from the motion of a quantum particle in a box. In retrospect, it seems like an obvious connection, but it’s exciting to begin to uncover the mathematical backbone behind this reciprocity.”

Batygin also admits that the Schrödinger Equation though a good explanation “cannot serve as a general replacement for more complex numerical simulations … [but] can be meaningfully used to provide qualitative context for numerical results”.

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