Energy levels in quantum well structures

In summary, the conversation discusses the use of Matlab to solve an eigenvalue equation and obtain energy levels in a quantum well structure. The equation is shown for both even and odd modes and can be numerically solved using the depth of the potential well and the effective mass. A possible resource for obtaining the code is suggested as the book "Quantum Wells, Wires and Dots" by Paul Harrison.
  • #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
I think you can get the code from the book titled 'quantum wells, wires and dots' written by paul harrison
 

FAQ: Energy levels in quantum well structures

What are quantum well structures and how do they relate to energy levels?

Quantum well structures are thin layers of semiconductor material that have a lower bandgap than the surrounding material. This creates a potential well for electrons, allowing for the manipulation of their energy levels. The energy levels in a quantum well structure are determined by the thickness and composition of the layers.

How do energy levels in quantum well structures differ from traditional energy levels in bulk materials?

In traditional bulk materials, energy levels are continuous and closely spaced. In quantum well structures, the energy levels are discrete and widely spaced due to the confinement of electrons within the potential well. This allows for more precise control over the energy states of electrons.

What factors affect the energy levels in quantum well structures?

The energy levels in quantum well structures are primarily influenced by the well width, barrier height, and composition of the layers. These factors determine the depth and shape of the potential well, which in turn affects the energy levels of electrons within the structure.

How are energy levels in quantum well structures measured and observed?

Energy levels in quantum well structures can be measured and observed through various techniques, such as photoluminescence and photocurrent spectroscopy. These methods involve exciting the electrons in the structure and analyzing the resulting emission or current to determine the energy levels.

What are the practical applications of energy levels in quantum well structures?

Quantum well structures have a wide range of applications, including in optoelectronic devices such as lasers and light-emitting diodes (LEDs). They also play a crucial role in the development of quantum computing and information processing technologies.

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