# Finite well penetration depths dependence on Well Length

• PsychonautQQ
In summary, in the finite square well, energy and wavelength are inversely proportional as the well size decreases. This leads to a smaller wavelength and greater energy, allowing for deeper penetration. However, the well size also decreases, which can affect the overall penetration length. It is recommended to work through the solution of the finite square well to fully understand this relationship.
PsychonautQQ
So in the infinite well Energy is proportional to 1/L^2, so I'm assuming in the finite well there is some sort of similar relation. So as the L decreases, the energy increases, so the wavelength decreases. Decreasing the wavelength means more energy, so it should penetrate further, but also if you draw the situation a smaller wavelength will make it penetrate less far, although the well also is getting smaller so blahh I'm trying to figure out how all this adds up. Thanks!

PsychonautQQ said:
but also if you draw the situation a smaller wavelength will make it penetrate less far

What do you mean by this? I don't think it's correct.

I suggest you actually work through the solution of the finite square well and see how the penetration length of the ground state wave function depends on L.

## What is a finite well penetration depth?

A finite well penetration depth refers to the distance from the surface of a well to the point where the concentration of a substance reaches its maximum value. It is an important factor in determining the effectiveness of a well in extracting or containing a substance.

## How does the well length affect the finite well penetration depth?

The well length plays a significant role in determining the finite well penetration depth. As the well length increases, the penetration depth also increases, allowing for a larger volume of substance to be extracted or contained.

## What factors influence the dependence of finite well penetration depth on well length?

The dependence of finite well penetration depth on well length can be influenced by various factors such as the properties of the substance being extracted or contained, the permeability of the surrounding material, and the flow rate of the substance.

## Why is it important to understand the dependence of finite well penetration depth on well length?

Understanding the relationship between finite well penetration depth and well length is crucial in designing effective well systems for extracting or containing substances. It can also help in predicting the behavior of substances in the subsurface environment.

## How can the finite well penetration depth be calculated?

The finite well penetration depth can be calculated using mathematical models that take into account various parameters such as the well length, the properties of the substance, and the surrounding environment. These models can provide an estimate of the penetration depth for different well lengths.

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