Schrodinger Equation Research Question

In summary: What textbooks have you studied, for example? Have you studied wave mecahnics and/or the Dirac Formalism?
  • #1
Eliot_Abramo
8
1
Hey guys,
I have had my eye on quantum mechanics for a while now and finally decided that I have a large enough understanding of the concept/math/theories behind it to write a research paper on it, specifically Schrodinger Equation. But I am having a hard time finding a good research question...

I was thinking something maybe along the lines of:
How did the Schrodinger wave equation contribute to the current quantum mechanics model of waves?
or
The evolution of Quantum mechanics theories over time (Niels Bohr, Albert Einstein, Louis de Broglie and Erwin Schrodinger)

The research paper should be around 4000 words so I need a question that is precise but broad enough for me to write 4000 words on. I was hoping that (with the help of the people on this forum) I could find a mathematics oriented research question. No this is not a school related work, but after talking to some of my teachers they recommended a word count of 4000 words, unfortunately they too didn't have any ideas vis-a-vis research questions.

Thanks in advance for any help or tips, anything that can help is much appreciated!
 
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  • #2
You could present the background as to why the Schrödinger equation is a wave equation. That can include the history of the wave equation as well as the context which led Schrödinger to his equation.
 
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  • #3
Thanks for the reply.
That seems like an interesting topic but how would you structure something like this in a 4000 word essay?
 
  • #4
Eliot_Abramo said:
Thanks for the reply.
That seems like an interesting topic but how would you structure something like this in a 4000 word essay?
I guess that's up for you to figure out. I'm not sure where the difficulty lies for you. Do you think that 4000 words is too much or too little?
 
  • #5
Well according to previous research paper that I've read in regards to the topic, I think that 4000 words is the right amount for a good, structured essay.
 
  • #6
What is your purpose in writing this essay?
 
  • #7
I want to study quantum mechanics and engineering in the future, so since I have a lot more free time due to most of my classes being canceled for Covid reasons, I thought that it would be a good idea to do some independent research.

Ultimately, I want to do some research into something Quantum Mechanics related.
 
  • #8
Eliot_Abramo said:
I want to study quantum mechanics and engineering in the future, so since I have a lot more free time due to most of my classes being canceled for Covid reasons, I thought that it would be a good idea to do some independent research.

Ultimately, I want to do some research into something Quantum Mechanics related.
Why not start with a 100-word essay here on what you have studied so far and what level of understanding of QM you have reached?

Which textbooks have you studied, for example? Have you studied wave mecahnics and/or the Dirac Formalism?
 

1. What is the Schrodinger equation?

The Schrodinger equation is a mathematical equation that describes how quantum systems, such as atoms and molecules, evolve over time. It is a fundamental equation in quantum mechanics and is used to calculate the probability of finding a particle in a certain location at a certain time.

2. Who is Schrodinger and why is this equation named after him?

Erwin Schrodinger was an Austrian physicist who developed the Schrodinger equation in 1926. He was one of the pioneers of quantum mechanics and his work greatly contributed to our understanding of the behavior of subatomic particles. The equation is named after him as he was the first to propose it as a way to describe the wave-like behavior of particles.

3. What is the significance of the Schrodinger equation in modern physics?

The Schrodinger equation is a cornerstone of modern physics and is used to understand the behavior of particles at the quantum level. It has been applied in various fields such as quantum chemistry, solid-state physics, and particle physics, and has been instrumental in developing technologies such as transistors and lasers.

4. How is the Schrodinger equation solved?

The Schrodinger equation is a complex mathematical equation that can be solved using various techniques such as numerical methods, perturbation theory, and variational methods. In some cases, an exact analytical solution can be obtained, but in most cases, approximations are used to find solutions.

5. What are some current research areas involving the Schrodinger equation?

There is ongoing research in using the Schrodinger equation to study new materials and their properties, as well as to understand the behavior of particles in extreme conditions such as in black holes. Additionally, there is a growing interest in using the equation in the development of quantum computing and other quantum technologies.

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