Schrodinger Equation Research Question

[Eliot_Abramo]

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 Schrödinger 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 Schrödinger 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 Schrödinger)

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!

 

[DrClaude]

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.

 

[Eliot_Abramo]

Thanks for the reply.
That seems like an interesting topic but how would you structure something like this in a 4000 word essay?

 

[DrClaude]

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?

 

[Eliot_Abramo]

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.

 

[gleem]

What is your purpose in writing this essay?

 

[Eliot_Abramo]

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.

 

[PeroK]

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?