The History and Development of Schrodinger's Wave Equation

In summary, the history and development of Schrödinger's wave equation can be traced back to Einstein's idea about the quantum nature of light, followed by deBroglie's hypothesis that this may also apply to matter. With his expertise in wave mechanics, Schrödinger was able to turn this hypothesis into a wave equation, known today as Schrödinger's equation. This was after his initial attempt with the relativistic Klein-Gordon equation, which proved to be unstable due to negative energy solutions. Schrödinger's equation was initially met with opposition from those advocating for matrix mechanics, but its success in treating multi-electron atoms solidified its place as the preferred approach in chemistry. It was later
  • #1
Entropia
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"The History and Development of Schrodinger's Wave Equation"

i am taking a class in "the history of chemistry" and i chose to write a paper on "the history and development of schrodinger's wave equation"...

does anybody have any suggestions on what kind of topics i should include?
 
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Originally posted by Entropia
i am taking a class in "the history of chemistry" and i chose to write a paper on "the history and development of schrodinger's wave equation"...

does anybody have any suggestions on what kind of topics i should include?

well, definitely include Einsteins idea about the quantum nature of light ([itex]E=h\nu[/itex])

from there, deBroglies hypothesis that the same thing may apply to matter

from there, it was an easy step for Schrödinger (who was one of the foremost experts on wave mechanics) to turn this hypothesis into a wave equation.

it is worth mentioning that Schrödinger first wrote down what we now call the Klein-Gordon equation, which is a relativistic wave equation, but abandoned this approach, because it seemed to lead to negative energy solutions, which lead to instabilities of the theory. so he turned to the nonrelativistic version, what we call Schrödinger's equation today.

also worth mentioning is how, while Schrödinger was doing all this, Heisenberg and Born were developing matrix mechanics, a completely different approach to quantum mechanics. for a little while, the entire field was split into two camps, the matrix mechanics people and the wave mechanics people, and they would make insults about each others theories. at the time, people thought one theory must be wrong, and only one would survive.

another thing worth mentioning is that the variation method of approximation in quantum mechanics was formulated in Schrödinger's wave mechanics, and it was the first successful quantum treatment of a multi-electron atom. Bohr's theory (quantize the action) was completely unsuccessful for Helium, and no one knew how to use Heisenberg's and Born's matrix mechanics on the hydrogen atom (perturbation theory doesn't work so well), so this was a great success for wave mechanics, and convinced a lot of people that it was correct. for this reason, the chemist will almost exclusively work with Schrödinger's wave mechanics, and never with Heisenberg's matrix mechanics.

then Schrödinger derived an equivalence between matrix mechanics and wave mechanics. von Neumann and others made this into a rigorous proof, known as the Stone-von Neumann theorem, and ever after, any physicist has felt free to use whichever is more convenient for the problem at hand. for us, they are not two different theories, but rather two different ways of writing the same theory, Quantum Mechanics.

in fact, today, we use Dirac's bra-ket notation, which can be used for either wave mechanics or matrix mechanics (these days, the fact that they are the same is obvious to anyone. the only difference between the approaches is whether the time dependence lives in the operators or the states, and you change from one to the other by multiplying by [itex]e^{iHt}[/itex])
 
  • #3


Schrodinger's wave equation is a fundamental equation in quantum mechanics that describes the behavior of particles at the atomic and subatomic level. It was developed by Austrian physicist Erwin Schrodinger in 1926 and has since become an essential tool for understanding the behavior of matter at the quantum level. The history and development of this equation is a fascinating story that involves the contributions of many scientists and the evolution of our understanding of the quantum world.

One important topic to include in your paper could be the historical context in which Schrodinger developed his equation. This includes the state of physics at the time, the existing theories and experiments that led to the need for a new equation, and the key players involved in the development of quantum mechanics. This will give your readers a better understanding of the significance of Schrodinger's work and the impact it had on the field of physics.

Another important aspect to cover is the development of Schrodinger's equation itself. This could include the key insights and breakthroughs that led Schrodinger to his famous equation, as well as the mathematical concepts and tools he used to formulate it. It would also be interesting to discuss the challenges and criticisms that Schrodinger faced in developing his equation and how he addressed them.

You could also discuss the implications and applications of Schrodinger's wave equation. This could include its role in explaining the behavior of particles such as electrons and photons, and its applications in fields such as quantum chemistry and quantum computing. It would also be interesting to mention how Schrodinger's equation has been used in other areas of physics, such as in the study of waves and oscillations.

Lastly, you could discuss the impact of Schrodinger's wave equation on the development of quantum mechanics as a whole. This could include the contributions of other scientists, such as Werner Heisenberg and Max Born, and how their work built upon and expanded Schrodinger's equation. You could also mention the debates and controversies surrounding the interpretation of the equation, such as the famous Schrodinger's cat thought experiment.

In conclusion, the history and development of Schrodinger's wave equation is a rich and complex topic that encompasses the contributions of many scientists and the evolution of our understanding of the quantum world. By covering these key topics, your paper will provide a comprehensive overview of the significance and impact of this fundamental equation in the field of physics.
 

1. What is Schrodinger's Wave Equation?

Schrodinger's Wave Equation is a mathematical equation that describes the evolution of a quantum mechanical system over time. It was developed by Austrian physicist Erwin Schrodinger in 1926 as a way to describe the wave-like behavior of particles, and is a fundamental equation in the field of quantum mechanics.

2. How did Schrodinger develop his wave equation?

Schrodinger developed his wave equation by combining the principles of classical mechanics and wave theory. He was inspired by the work of French physicist Louis de Broglie, who proposed that particles have both wave-like and particle-like properties. Schrodinger's equation was also influenced by the ideas of Albert Einstein and Max Planck on the quantization of energy.

3. What is the significance of Schrodinger's Wave Equation?

Schrodinger's Wave Equation is significant because it provided a way to mathematically describe the behavior of particles at the quantum level. It allowed for the calculation of probabilities of a particle's position and momentum, and helped to explain the phenomenon of wave-particle duality. The equation is also used in many practical applications, such as in the development of new technologies and in understanding the behavior of atoms and molecules.

4. How has Schrodinger's Wave Equation evolved over time?

Schrodinger's Wave Equation has undergone several modifications and extensions since its initial development. One of the most notable advancements was the introduction of the time-dependent version of the equation, which allows for the calculation of a particle's behavior over time. Other developments have focused on incorporating more complex systems, such as multiple particles and interactions with electromagnetic fields.

5. What impact has Schrodinger's Wave Equation had on modern science?

Schrodinger's Wave Equation has had a profound impact on modern science, particularly in the fields of quantum mechanics, atomic and molecular physics, and materials science. It has also played a significant role in the development of technologies such as lasers, transistors, and computer chips. The equation continues to be an important tool for scientists in understanding and predicting the behavior of particles at the quantum level.

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