# Potential well solutions question

• physicsjock
In summary, a potential well is a region of space where particles are confined by a potential energy barrier, creating a "well" in the potential energy graph. Examples include the nucleus of an atom and potential energy wells created by magnetic fields or gravity. In quantum mechanics, the solutions to the Schrödinger equation describe the allowed energy levels and wave functions of particles in a potential well. The types of solutions depend on the shape and depth of the potential energy barrier, and they have applications in fields such as quantum mechanics, solid-state physics, and nanotechnology. This is important for understanding and developing new technologies like transistors and quantum computers.
physicsjock
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1) what is d, if d=0 then you have the same answer!

2) if it had to do with passing through the barrier shouldn't the depth u be of interest as well? in the sense that there is no passing through an infinite barrier, but if u is not quantatively involved then passing to the limit u goes to infinity will not end you up in the case of the infinite well.

## What is a potential well?

A potential well is a concept in physics that refers to a region of space where particles, such as atoms or electrons, are confined by a potential energy barrier. This barrier creates a "well" in the potential energy graph, and the particles are trapped within this well.

## What are some common examples of potential wells?

A common example of a potential well is the nucleus of an atom, which traps the electrons within its potential energy barrier. Other examples include the potential energy wells created by magnetic fields, gravity wells, and potential energy wells in solid materials.

## How do potential well solutions relate to quantum mechanics?

In quantum mechanics, the wave function of a particle is described by a time-independent Schrödinger equation. The solutions to this equation are known as "wave functions" or "eigenfunctions", and they represent the probability distribution of finding a particle in a certain location. In the case of a potential well, the solutions to the Schrödinger equation describe the allowed energy levels and wave functions of particles confined within the well.

## What are the types of potential well solutions?

The types of potential well solutions depend on the shape and depth of the potential energy barrier. The most common types include the infinite square well, the finite square well, the harmonic oscillator potential well, and the Coulomb potential well.

## How do potential well solutions impact real-world applications?

Potential well solutions have a wide range of applications in various fields, such as quantum mechanics, solid-state physics, material science, and nanotechnology. They are used to understand and predict the behavior of particles in confined spaces, which is crucial for the development of new technologies, such as transistors and quantum computers.

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