A new discovery by a researcher from the California Institute of Technology has indicated that Schrödinger Equation is useful for explaining how certain types of astronomical structures evolve in the long-term. 

Astrophysical Disk Evolution

Gigantic astronomical bodies are usually encircled by clusters of smaller celestial bodies revolving around them. For instance, swarms of stars orbit supermassive black holes, and the stars themselves have a huge amount of space debris, ice, and rock orbiting them.

The massive volumes of material form in round, flat disks due to gravitational force and can be as big as the solar system or measuring many light-years in width. The astrophysical disks gradually evolve to display distortions in a large scale, which warp and bend like pond ripples.

Astronomers have been long puzzled by how the warps appear and flourish. The technique is also too complex to be modeled by computer simulations, not to mention expensive.

Researcher Konstantin Batygin from Caltech, who is also the theorist to have first proposed Planet Nine's existence, recently took the help of an approximation scheme, referred to as perturbation, to create an easy disk evolution representation in mathematics.

Perturbation helped to model a disk as a concentric wire series, among whom a slow orbital angular momentum exchange takes place. When perturbation was used to model the evolution of disk, the researcher found surprising results.

"When we do this with all the material in a disk, we can get more and more meticulous, representing the disk as an ever-larger number of ever-thinner wires," said Batygin. "Eventually, you can approximate the number of wires in the disk to be infinite, which allows you to mathematically blur them together into a continuum."

Batygin was astonished that his calculations led to the Schrödinger Equation.

Schrödinger Equation

"The Schrodinger equation is used to find the allowed energy levels of quantum mechanical systems (such as atoms, or transistors). The associated wavefunction gives the probability of finding the particle at a certain position. The solution to this equation is a wave that describes the quantum aspects of a system," PhysLink explains.

In simpler words, Schrödinger Equation is the primary equation of quantum mechanics, which is the division of physics that governs the behavior of tiny particles that make up the universe on the scale of atoms and subatomic particles.

Equations that describe the world of quantum are usually capped at the subatomic realm. It means that the mathematics that is true for small scales may not be true for those at a large scale.

Schrödinger Equation Can Explain Disk Evolution

The study, which has been published in the journal Monthly Notices of the Royal Astronomical Society on March 5, however, indicates warps that occur in a large scale in astrophysical disks have a behavior similar to tiny particles.

Therefore, according to Batygin, the same mathematical equation that explains single quantum particle behavior, if it was bouncing to and fro between a disk's outer and inner edge, can also be used to explain warp propagation inside disk material.

The discovery that the Schrödinger Equation can be used to explain astrophysical disks' evolution for a long-term should be beneficial for researchers who model huge-scale phenomena such as these. Batygin also added that it is interesting that two divisions of physics, which seem unrelated, can be ruled by the same type of mathematics.