Schrödinger Equation May Have A Solution at Last

by Rudra Mehta


Schrödinger Equation May Have A Solution at Last

January 9, 2021

Is the cat dead or alive, or both? This evergreen question might finally have an answer, thanks to scientists at Freie Universität, Berlin.

If you’re a fan of The Big Bang Theory and have those ‘nerdy’ tendencies like Sheldon, chances are you would have heard of the famous ‘Schrödinger’s Cat Experiment’. The experiment was born out of a need to explain the Wave Equation proposed by Erwin Schrödinger as a grouping of the Copenhagen Interpretation. After years of uncertainty, scientists seemed to have cracked the Schrödinger Equation, thanks to AI.

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”Schrödinger's Cat" was originally meant to mock quantum theory. However, quantum scientists have long seen the thought experiment as a challenge.

The Cat Dilemma

So, who is Schrödinger’s Cat? Shady, the Cat, was Erwin’s animal companion. One fine day, Schrödinger conversed with Albert Einstein about the Copenhagen Interpretation’s inconsistencies for quantum mechanics, quantum chemistry to be precise. He created an imaginary experiment to demonstrate how quantum theory can be misinterpreted, and a minor deviation can lead to absurd results.

When Schrödinger postulated his Equation, scientists believed that only conscious observers (constant observation) could achieve single state quantum particles. What this means is that a quantum particle collapses to a single state when monitored by an entity. To disprove this, Schrödinger hypothetically placed a cat in a closed box with a radioactive substance. The substance triggers a Geiger counter (an instrument used to measure ionizing radiation), releasing a vial of poison with an explosion, thus killing the cat in the box.

Quantum mechanics governs the radioactive decay of that substance. So, the substance (in this case, its atoms) is decaying and not decaying at the same time. If the conscious observer theory is applied, there can be no decay since the box is sealed. Hence, the cat is technically both dead and alive at the same time. This cannot happen in real life and thus, shows that wavefunction collapse is not just a result of conscious observers.

Schrödinger proposed this thought-experiment to demonstrate how ridiculous quantum super-position is.  Basically the multiple states of a single atom (decayed and not decayed) causes a cat to be in multiple states (living and dead).

However, this interpretation is disproved, most elegantly, by your setup of a radioactive atom, Geiger counter, amplifier, a charge of gun powder, and a cat in a box. The psi-function of the system contains the cat, both alive and dead. Is the cat's state-determined only when a physicist investigates the situation at some definite time?

- Albert Einstein in his congratulatory address to Schrödinger

The Schrödinger Equation

Why is this Equation significant, other than to understand Sheldon Cooper’s rant? You see, predicting every molecule’s physical and chemical properties based on the position and arrangement of their atoms in space forms the basis of quantum chemistry. Schrödinger’s Equation is just one, but the most efficient way of determining this. In theory, that is, as it is complicated in practice.

Schrödinger Equation is a wavefunction. A wave function describes an electron’s behavior in a molecule. And since the wavefunction consists of multiple dimensions, it is near impossible to calculate all instances of a single electron’s behaviour, individually and with each other. Quantum chemistry in its current state fails to explain the wave function, only approximating the energy instead.

Quantum Physicists were limited to just a handful of accurate calculations involving only a few atoms, given the complex mathematics at play. Thanks to deep learning methods and AI, this is soon about to change.

Schrödinger's Cat
Schrödinger's Cat is a brilliant example of how quantum mechanics can be easily visualised as abstract concepts.

So, What’s the Solution?

Back to the topic at hand, scientists at Freie Universität, Berlin, have synthesised a method to calculate Schrödinger’s Equation’s ground state accurately. Researchers have created a neural network using AI to map and plot each instance of the function at any given instant. Here is what the key designer of the project had to say:

Escaping the usual trade-off between accuracy and computational cost is the highest achievement in quantum chemistry. Right now, the most famous such outlier is the extremely cost-effective density functional theory. We are confident that deep "Quantum Monte Carlo," the approach we are proposing, could be equally, if not more successful. It offers unprecedented accuracy at a still acceptable computational cost.

- Dr. Jan Hermann, Freie Universität
Measuring of a Quantum System Using Schrodingers Cat
Since the cat in the box (top left) is in a superposition that means it can be in numerous different states (e.g. dead and/or alive) and is marked with a quantum tag. The photo taken of the cat is entangled with the situation inside of the box. We can decide the fate of the cat by processing the photo in a certain way (bottom left), or we can keep it in superposition by restoring the quantum tag using a different process (bottom right). Credit: Associate Professor Holger F. Hofmann and Emma Buchet/Hiroshima University.

Instead of using the wave function for each calculation, the task is handed over to the AI, who spends some time learning the electron patterns and their relative positions around the nuclei. Electronic wave functions have a unique feature known as anti-symmetry. Wavefunctions flip their signs when electrons are swapped. People would be aware of this without realising, as this is Pauli’s Exclusion Principle, taught to all of us in high school! This is also why the method has been dubbed ‘PauliNet’.

Scientists admit that the neural network is still primitive and will take some time to reach the industrial standards, paving the way for extensive research on molecular and material sciences.

The research is still in its nascent stages. Always, it will be a substantial boost in enabling quantum mechanics usage for a host of applications, including, but not limited to, space materials, dark matter, and invisible radiation. All we can do now is wait and watch.

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1 comment

White Woods January 9, 2021 - 9:03 pm

This article was really interesting n i am hoping get more useful and interesting articles like this in the future. I am following your page on Instagram and I check out every post and reels because it piques my interest in scientific stuff.


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