Electron in a triangular quantum well with triangular barrier

[Drone0]

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.

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.

 

[Nate810]

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.