Proving the Schrodinger Equation

In summary, scientists were able to prove the accuracy of Schrodinger's equation through experiments that showed its predictions matched with the behavior of subatomic particles. These experiments also involved measuring the atomic spectra of elements like hydrogen. The accuracy of the experiments is based on repeating measurements to ensure the probabilities described by the equation are correct.
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thegroundhog
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TL;DR Summary
How were scientists able to do experiments to prove that the Schrodinger equation was correct?
How did scientists prove the accuracy of Schrodinger's equation to describe the behaviour of subatomic particles, especially in the 1920s? How do you monitor an electron's momentum and position when they are so small? Also, if the Schrodinger equation just describes probabilities, is the accuracy of the experimenting based on doing the same measurements over and over to make sure the probabilities are correct (in the same way to check the heads/tails probability of a coin, the more measurements the better, as it will tend towards 50%)?
 
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thegroundhog said:
Summary:: How were scientists able to do experiments to prove that the Schrodinger equation was correct?

How did scientists prove the accuracy of Schrodinger's equation to describe the behaviour of subatomic particles, especially in the 1920s? How do you monitor an electron's momentum and position when they are so small? Also, if the Schrodinger equation just describes probabilities, is the accuracy of the experimenting based on doing the same measurements over and over to make sure the probabilities are correct (in the same way to check the heads/tails probability of a coin, the more measurements the better, as it will tend towards 50%)?
You probably need to read the history of QM to clarify the exact sequence of events. In modern QM, the Schrodinger equation can be derived from some expected properties of the time evolution operator: see, for example, Modern Quantum Mechanics by J..J. Sakurai.

The acid test is not direct measurements of an electron, but the prediction of the atomic spectra for hydrogen etc. In this case, even the different energy levels themselves are not measured directly but inferred from the atom's spectrum (i.e. the measurement is of the wavelength (or frequency) of the emission and absorption spectrum).
 
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FAQ: Proving the Schrodinger Equation

What is the Schrodinger Equation?

The Schrodinger Equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. It mathematically represents the behavior of particles at the atomic and subatomic level.

Why is it important to prove the Schrodinger Equation?

Proving the Schrodinger Equation is important because it provides a theoretical basis for understanding the behavior of quantum systems. It allows for the prediction of the behavior of particles and their interactions, leading to advancements in fields such as chemistry, materials science, and technology.

How was the Schrodinger Equation developed?

The Schrodinger Equation was developed by Austrian physicist Erwin Schrodinger in 1926. He combined the concepts of wave mechanics and classical mechanics to create a mathematical equation that could describe the behavior of quantum systems.

What evidence supports the accuracy of the Schrodinger Equation?

There have been numerous experiments and observations that support the accuracy of the Schrodinger Equation. For example, it accurately predicts the energy levels of electrons in atoms and the behavior of particles in a double-slit experiment.

Are there any limitations to the Schrodinger Equation?

While the Schrodinger Equation is a powerful tool for understanding quantum systems, it does have limitations. It cannot fully explain certain phenomena such as the collapse of the wave function and the measurement problem. Additionally, it does not account for the effects of relativity and gravity.

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