Electron in a triangular quantum well with triangular barrier

In summary, the square quantum well problem involves solving the Schrödinger equation to obtain the energy levels and wavefunctions of an electron confined to a one-dimensional quantum well. To solve this problem, you need to define the potential energy profile of the quantum well, solve the Schrödinger equation, and then use the obtained wavefunctions to calculate the probability density distribution and capacitance-voltage profile. You could also use a software package such as MATLAB or Python to assist with the coding process.
  • #1
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Moved from a technical forum, so homework template missing
Hi, it's been so long since I learned quantum mechanics. So the only thing I can solve now is the square quantum well problem.
But I need help because I have to solve this problem of quantum well.

KakaoTalk_20191023_122535839.png

I tried some calculation but not far.I try to draw the capacitance-voltage profile by drawing the probability distribution when the electron is in the quantum well in the figure, and by finally calculating the variation of external electric field.
Is ∫|ψ|^2dx =1 in well?
How do I get started and how do I code my programs?

I really don't remember anything at all... I'm sorry for the lack of context in this questions.
 
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  • #2
The square quantum well problem is a classic example of a one-dimensional quantum system. It models the motion of an electron confined to a region of space (the quantum well) with certain boundary conditions. The solution of this problem involves solving the Schrödinger equation and obtaining the energy levels and wavefunctions of the electron in the quantum well. To solve this problem, you need to start by defining the potential energy inside the quantum well, which is typically a piecewise constant function. You then need to solve the time-independent Schrödinger equation for this potential energy profile to get the energy eigenvalues and wavefunctions for the electron in the quantum well. Once you have obtained the wavefunctions, you can calculate the probability density distribution and the capacitance-voltage profile of the quantum well using the wavefunctions. To do this, you need to integrate the square of the wavefunction over the region of the quantum well. This integral should indeed be equal to one.If you are having difficulty coding up the solution to this problem, you could consider using a software package such as MATLAB or Python that has built-in functions for solving the Schrödinger equation and calculating the wavefunctions and probability density distributions.
 

1. What is a triangular quantum well?

A triangular quantum well is a three-sided potential energy structure that confines electrons in a two-dimensional space. It is created by sandwiching a thin layer of a semiconducting material between two layers of a material with a larger bandgap.

2. What is a triangular barrier?

A triangular barrier is a potential energy structure that creates a barrier for electrons within a triangular quantum well. It is created by varying the thickness of the semiconducting layer, causing a change in the bandgap and creating a potential energy barrier.

3. How does an electron behave in a triangular quantum well with triangular barrier?

An electron in this system behaves as a wave and is confined to the triangular quantum well. It will also experience a potential energy barrier at the edges of the well, causing it to exhibit quantum mechanical properties such as wave interference.

4. What applications does this system have?

This system has potential applications in semiconductor devices, such as transistors and lasers, as well as in quantum computing and optoelectronics. It can also be used to study the quantum behavior of electrons in confined systems.

5. How does the shape and size of the triangular quantum well and barrier affect the behavior of the electron?

The shape and size of the triangular quantum well and barrier can affect the energy levels and wave functions of the electron, which in turn affect its behavior and properties. For example, a smaller well and barrier would result in a higher energy level and a shorter wavelength for the electron's wave function.

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