# Kronig-Penney Model: Understanding Electron Potential Energy

• manofphysics
In summary, the conversation discusses the modification of the potential energy of an electron in the Kronig-Penney model. The original model, shown in fig 1, had a negative potential energy for the electron. However, in Charles Kittel's book, the potential was modified to be a square potential with a positive energy, as shown in fig 2. This modification raises questions about the accuracy of the Schrodinger equation solutions and whether they would change in the respective regions. The note provided also mentions that the value of Vo (the potential energy) is taken to be negative in one source while positive in another, leading to different solutions. Ultimately, the conversation highlights a discrepancy in the understanding of the potential energy in the Kronig-P

#### manofphysics

We know electron has potential energy as shown in fig 1 .
Now in my book ( Charles Kittel) it is written that kronig and penney modified this to be a square potential as shown in fig 2.
How is the potential in fig 2( inkronig penney model) drawn to be positive (Vo) if in figure 1 it is shown to be negative ( and rightly so,as in my opinion, potential energy of electron should be negative in presence of positive charge)?
Will the Schrodinger eqn solutions not change in the resp. regions if we arbitrarily change the sign of the potential energy to positive as has been done in kittel?
And one note: http://en.wikipedia.org/wiki/Partic...tice_(periodic_potential)#Kronig-Penney_model :here Vo is taken to be negative and hence Schrodinger eqn soln is different in -b<x<0 from the one given in Kittel.Is this and kittel both right?
Fig 1 and fig2 are attached

#### Attachments

• fig 1.jpg
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• fig 2.gif
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Man of physics, come on, that's just a point of adding or subtracting a constant energy!

## What is the Kronig-Penney model?

The Kronig-Penney model is a theoretical model used to understand the behavior of electrons in a periodic potential. It helps to explain how electrons move through a crystal lattice by considering the potential energy barrier between the atoms in the lattice.

## How does the Kronig-Penney model explain electron energy levels?

The Kronig-Penney model describes electrons in a crystal lattice as having energy levels that are quantized, or discrete. These energy levels are determined by the periodic potential of the lattice and the allowed energy bands within it.

## What is the significance of the Kronig-Penney model in solid state physics?

The Kronig-Penney model is an important tool in understanding the properties of solid materials, such as metals and semiconductors. It helps to explain phenomena such as electrical conductivity and the behavior of electrons in energy bands.

## What are the limitations of the Kronig-Penney model?

The Kronig-Penney model is a simplified model and does not take into account all the factors that influence the behavior of electrons in a crystal lattice. It also assumes that the potential energy is constant throughout the lattice, which may not always be the case in real materials.

## How is the Kronig-Penney model used in practical applications?

The Kronig-Penney model is used in various fields, including materials science and solid state physics, to understand and predict the behavior of electrons in different materials. It has also been used in the development of new materials for electronic devices and in quantum mechanics research.