What is the basic assumption of Kronig Penney model?
What is the basic assumption of Kronig Penney model?
The essential behaviour of electron may be studied by periodic rectangular well in one dimensional which was first discussed by Kronig Penney in 1931. It is assumed that when an electron is near the positive ion site, potential energy is taken as zero.
What is periodic potential of lattice?
In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the crystal creating an electromagnetic field so electrons are subject to a regular potential inside the lattice.
What does Bloch function represent physically?
The Bloch states are eigenfunctions of the translational symmetry operator of the crystal. These states satisfy the periodicity of the crystal involved.
What is the effect of periodic potential on the energy of electrons in metal explain it on the basis of Kronig Penney model and explain the formation of energy bands?
when a particular potential energy is supplied on a metal then the energy of the electrons present in the valence shell increases and they migrate to the outer orbit. Explanation: Kroinig penney model is a useful model which is used to determine the position of the electron in a two dimensional plane.
What is the Kronig Penney model What does it represent?
The Kronig-Penney model [1] is a simplified model for an electron in a one-dimensional periodic potential. The possible states that the electron can occupy are determined by the Schrödinger equation, k) and the electron density of states.
What are the conclusions of kronig Penny model?
We have concluded in the Kronig-Penny model that the energy discontinuities in a monatomic one-dimensional lattice occur when k = (nπ/a), where n is any positive or negative integer.
What is Kronig Penney equation?
The Kronig-Penney model [1] is a simplified model for an electron in a one-dimensional periodic potential. The possible states that the electron can occupy are determined by the Schrödinger equation, This form can be used to plot the dispersion relation and the density of states for the Kronig Penney model.
Why do we need Bloch theorem?
Plane waves can be seen as a grid basis in momentum space, motivated by Bloch’s theorem. As such they extend over the whole real space and are thus particularly suited for periodic boundary conditions in solid state calculations.
What are the salient features of Kronig Penney model?
The Kronig-Penney model [1] is a simplified model for an electron in a one-dimensional periodic potential. The possible states that the electron can occupy are determined by the Schrödinger equation, In the case of the Kroning-Penney model, the potential V(x) is a periodic square wave.
Why do we use Bloch theorem?
Applications and consequences The most common example of Bloch’s theorem is describing electrons in a crystal, especially in characterizing the crystal’s electronic properties, such as electronic band structure. However, a Bloch-wave description applies more generally to any wave-like phenomenon in a periodic medium.
What are the conclusions of Kronig Penney model?
Hence we conclude that the total number of possible wave functions in any energy band is equal to the number of unit cells N. We have concluded in the Kronig-Penny model that the energy discontinuities in a monatomic one-dimensional lattice occur when k = (nπ/a), where n is any positive or negative integer.
Which one is correct for free electron theory?
Explanation: The free electrons move randomly in all directions. The free electrons collide with each other and also with the lattice Elastically, without loss in energy.
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