Schrödinger's equation, its derivation

In summary, physicist Richard Feynman discussed the origin of the Schrödinger equation, stating that it cannot be derived from existing knowledge and was instead created by Schrödinger himself. It is similar to other empirical formulas, like the Balmer formula and Rydberg equation, and there is currently no theory behind it. It is possible that in the future, we may uncover the reason for its form, just as Bohr did for the Balmer formula.
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robertjford80
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Richard Feynman said:

Where did we get that (equation) from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger.

So does this mean that it is a equation like the Balmer formula or the Rydberg equation? There's no theory behind it, it's just an empirical formula? Did S just look at data and come up with an equation that fit the data? Is it possible that we will find out why the S equation is the way it is in the future, just as Bohr found out why the Balmer formula is the way it is?
 
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FAQ: Schrödinger's equation, its derivation

What is Schrödinger's equation and what does it describe?

Schrödinger's equation is a fundamental equation in quantum mechanics that describes the behavior of a quantum system over time. It is a differential equation that accounts for the wave-like behavior of particles and allows us to calculate the probability of finding a particle in a certain state.

How was Schrödinger's equation derived?

Schrödinger's equation was derived by Austrian physicist Erwin Schrödinger in 1925. He based his equation on the de Broglie hypothesis, which states that particles can exhibit wave-like behavior. Schrödinger used mathematical techniques to combine this idea with the principles of classical mechanics to create an equation that accurately describes the behavior of quantum systems.

What are the key components of Schrödinger's equation?

Schrödinger's equation consists of a time-dependent part, represented by the symbol ∂/∂t, and a spatial part, represented by the symbol ∇². The equation also includes the Hamiltonian operator, which represents the total energy of the system, and the wave function, which describes the quantum state of the system.

What are the implications of Schrödinger's equation?

Schrödinger's equation revolutionized our understanding of the behavior of particles at the atomic and subatomic level. It showed that particles can exhibit both wave-like and particle-like behavior, challenging the classical view of particles as solid, tangible objects. The equation also allows us to accurately predict the behavior of quantum systems, leading to advancements in fields such as chemistry, materials science, and electronics.

Are there any limitations to Schrödinger's equation?

While Schrödinger's equation is a powerful tool for understanding and predicting the behavior of quantum systems, it is not applicable to all systems. It does not take into account relativistic effects, and it cannot be used for systems with more than one particle. In these cases, more complex equations, such as the Dirac equation, must be used.

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