Eigenvalues for particle in finite square well

[poder17]

I am a second year physics student and have been set a homework assignment to solve a one dimensional time independant schrodinger equation in a finite square well using microsoft excel.
I understand the physics behind the situation but am not exactly sure how to use microsoft excel to solve the equation.
I need to present graphs of the normalised wavefunctions and the corresponding probability distributions.
I need to chose my own m (mass), L (length of well) and Vo so that there are four energy eigenvalues and then calculate and show these values.
Anyone who could help shed some light on this, your help would be greatly appreciaeted.

Thanks,
Joel

 

[CaptainQuaser]

put this in physics homework questions instead, and you will need to show an attempt at a solution.

 

[denian]

Hello Joel,

It is great to see that you are exploring the world of quantum mechanics and using computational tools like Microsoft Excel to solve problems. Solving the one dimensional time independent Schrodinger equation for a particle in a finite square well is a great exercise to understand the concept of energy eigenvalues and wavefunctions.

To start with, let me briefly explain the concept of energy eigenvalues for a particle in a finite square well. In quantum mechanics, energy eigenvalues refer to the possible energy states that a particle can occupy in a given system. In the case of a particle in a finite square well, the potential energy is defined as zero within the well and infinite outside the well. This creates a finite region where the particle can exist, and the energy levels within this region are known as energy eigenvalues.

Now, coming to the use of Microsoft Excel to solve the problem, there are a few steps you can follow. First, set up the one dimensional Schrodinger equation in Excel using the appropriate formulae for the potential energy and the Hamiltonian operator. Then, use the solver tool to numerically solve the equation and obtain the eigenvalues. You can then use these eigenvalues to calculate the corresponding wavefunctions and probability distributions.

To choose your own values for mass, length of the well, and potential energy, you can start with some reasonable values and then adjust them to get four distinct energy eigenvalues. This will require some trial and error, but it will give you a better understanding of the relationship between these parameters and the resulting energy levels.

Lastly, to present your results, you can use Excel to plot the wavefunctions and probability distributions as graphs. This will give you a visual representation of the solutions and help you analyze them better.

I hope this helps you get started with your assignment. If you have any further questions or need clarification, please don't hesitate to reach out. Keep exploring and learning about quantum mechanics, and good luck with your assignment!

Best regards,