Energy levels in quantum well structures

In summary, the conversation discusses the use of Matlab to solve the eigenvalue equation for a potential well, in order to obtain the energy levels. The equation can be solved numerically using the fzero command.
  • #1
starla
2
0
Does anyone knows how to solve the following eigenvalue equation using matlab? so as to obtain the energy levels in a quantum well structure.. or does anyone has the codes or knows where to find the codes to do so?

Eigenvalue equation:

tan(sq_root(2mE/hbar^2)*(d/2)) = sq_root((V-E)/E) for even mode (n=2,4,6...)

cot(sq_root(2mE/hbar^2)*(d/2)) = -sq_root((V-E)/E) for odd mode (n=1,3,5...)

where V is the depth of the potential well and m is the effective mass. The eignvalue equation shown above can be numerically solved to yield the energy levels E in a potential well.
 
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  • #2
starla said:
Does anyone knows how to solve the following eigenvalue equation using matlab? so as to obtain the energy levels in a quantum well structure.. or does anyone has the codes or knows where to find the codes to do so?

Eigenvalue equation:

tan(sq_root(2mE/hbar^2)*(d/2)) = sq_root((V-E)/E) for even mode (n=2,4,6...)

cot(sq_root(2mE/hbar^2)*(d/2)) = -sq_root((V-E)/E) for odd mode (n=1,3,5...)

where V is the depth of the potential well and m is the effective mass. The eignvalue equation shown above can be numerically solved to yield the energy levels E in a potential well.
Can't you just write, e.g.,

0 = tan(sq_root(2mE/hbar^2)*(d/2)) - sq_root((V-E)/E),

and use the fzero command.
 
  • #3
This can be done using MATLAB, a widely used software for scientific computing. There are several approaches to solving this type of eigenvalue equation in MATLAB, such as using the "eig" function or creating a custom algorithm. Additionally, there are many resources available online that provide codes for solving this type of problem. I suggest searching for "MATLAB code for solving eigenvalue equations in quantum well structures" to find relevant codes and resources. It is also important to note that the accuracy of the solutions will depend on the chosen numerical method and the parameters used in the calculation. I recommend consulting with a knowledgeable colleague or referencing literature in the field for guidance on selecting appropriate parameters and verifying the results.
 

1. What are quantum well structures?

Quantum well structures are artificially engineered materials that consist of thin layers of different materials, typically semiconductors, stacked on top of each other. These layers create a potential well for electrons, confining them in a specific region and allowing for control of their energy levels.

2. How do quantum well structures manipulate energy levels?

Quantum well structures manipulate energy levels by creating a potential well for electrons. The electrons are confined to a specific region within the structure, which leads to discrete energy levels, similar to those seen in atoms. By adjusting the thickness and composition of the layers, the energy levels can be controlled and tailored for specific applications.

3. What is the significance of energy levels in quantum well structures?

The energy levels in quantum well structures play a crucial role in determining the electronic and optical properties of the material. By controlling the energy levels, researchers can design materials with specific properties, such as high conductivity or efficient light emission, for use in various technological applications.

4. How are energy levels in quantum well structures measured?

Energy levels in quantum well structures can be measured using a variety of techniques, such as photoluminescence spectroscopy, which measures the light emitted from the material when excited by a laser. Other methods include electrical measurements, such as current-voltage measurements, and scanning tunneling microscopy.

5. What are some potential applications of quantum well structures?

Quantum well structures have a wide range of potential applications, including in optoelectronic devices such as lasers, light-emitting diodes, and solar cells. They are also being studied for use in quantum computing, as their discrete energy levels could be used to store and manipulate information. Additionally, they have potential in sensing and detection technologies, as well as in renewable energy technologies.

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