Calculating Lowest Energy Levels of a Rigid Spherical/Cubic Box

In summary, the conversation discusses determining the energy levels, degeneracies, and quantum numbers for an electron in a rigid spherical box and a rigid cubic box. The solution is expressed in multiples of ħ2/(2m0a2) and in electron Volt units. The conversation also mentions plotting the result on energy level diagrams and using Schrodinger's equation in spherical coordinates. The thread provides a link for how to use \LaTeX typsetting to post equations in the forum.
  • #1
quantumdude10
5
0

Homework Statement



Determine the four lowest energy levels, their degeneracies and quantum numbers of the wavefunctions for an electron in

i) a rigid spherical box of 2 Angstrom radius and,

ii) a rigid cubic box of the same volume

Express the result in multiples of ħ2/(2m0a2), and in electron Volt units. Plot the result on energy level diagrams and comment.


Homework Equations


Schroedinger's equation in spherical coordinates...


The Attempt at a Solution



Not sure how to solve 3d questions...
 
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  • #2
Welcome to Physics Forums.

How about we start with writing out Schrodinger's equation with the laplacian in spherical coordinates.

Do you know what the usual ansatz is for 3D spherically symmetric problems?
 
  • #3
you mean this one?

is there a way to post those equations to the body directly and not as an attachment?
 

Attachments

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  • #4
  • #5
quantumdude10 said:
you mean this one?
That's the one. Now, do you know the appropriate ansatz?
 

Related to Calculating Lowest Energy Levels of a Rigid Spherical/Cubic Box

1. What is the purpose of calculating the lowest energy levels of a rigid spherical/cubic box?

The purpose of calculating the lowest energy levels of a rigid spherical/cubic box is to understand the energy properties of a confined system and to predict the behavior of particles within the box. This can also be used to study the thermodynamics and statistical mechanics of the system.

2. How is the lowest energy level of a rigid spherical/cubic box calculated?

The lowest energy level of a rigid spherical/cubic box is calculated by solving the Schrödinger equation for the confined system, which takes into account the potential energy within the box and the wave function of the particles. This can be done numerically or analytically depending on the specific system.

3. What factors influence the lowest energy levels of a rigid spherical/cubic box?

The lowest energy levels of a rigid spherical/cubic box are influenced by various factors such as the size of the box, the shape of the box, the potential energy within the box, and the number and type of particles present in the box. Additionally, external factors such as temperature and pressure can also affect the energy levels.

4. How can the lowest energy levels of a rigid spherical/cubic box be used in practical applications?

The lowest energy levels of a rigid spherical/cubic box can be used in various practical applications such as in material science, where the behavior of particles in a confined space is important, or in the development of new technologies such as quantum computing. It can also be used to analyze and predict the behavior of gases and liquids in a closed container.

5. Are there any limitations to calculating the lowest energy levels of a rigid spherical/cubic box?

Yes, there are some limitations to calculating the lowest energy levels of a rigid spherical/cubic box. This method may not accurately represent the behavior of particles in a real system due to simplifications and assumptions made in the calculations. Additionally, the results may vary depending on the specific model and parameters used for the calculation.

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