how can I make a relation between it and triangular well plus schrodinger eq. in order to find eigenfunctions?MisterX said:You might want to look up Airy Functions.
This is described on the Wikipedia page (you may need to rescale x and y to get to the same differential equation though).Dirac62 said:how can I make a relation between it and triangular well plus schrodinger eq. in order to find eigenfunctions?
A triangular quantum well is a type of potential energy structure that is used in quantum mechanics to study the properties of electrons in a confined space. It consists of a triangular-shaped potential well, which creates a barrier for electrons to move in and out of the well.
Eigenfunctions and eigenvalues are mathematical concepts used to describe the behavior of quantum particles within a potential well. Eigenfunctions represent the stationary states of a particle, while the corresponding eigenvalues represent the energy levels associated with these states.
In the case of a triangular quantum well, the eigenfunctions are shaped like triangular waves and the eigenvalues correspond to the allowed energy levels of the particles within the well. These eigenfunctions and eigenvalues can be calculated using mathematical equations and are important in understanding the behavior of particles in this type of potential well.
Eigenfunctions and eigenvalues are essential in quantum mechanics as they provide a way to describe and understand the behavior of particles in confined spaces, such as in a triangular quantum well. They help determine the allowed energy levels and the probabilities of finding a particle in a particular state.
The study of eigenfunctions and eigenvalues in triangular quantum wells has led to advancements in technology, such as the development of quantum dot devices which have potential applications in quantum computing and telecommunications. Understanding the properties of particles in confined spaces is also important in fields like material science and nanotechnology.