The Kronig Penney model is a theoretical model used to describe the electronic band structure of a one-dimensional crystal. In reciprocal space, it allows us to visualize the periodicity of the crystal lattice and the allowed energy levels for electrons.
The Bloch theorem describes the behavior of electrons in a periodic potential, while the Kronig Penney model specifically focuses on a one-dimensional crystal with a periodic potential. The main difference is that the Kronig Penney model takes into account the potential barrier between lattice sites, which is not considered in the Bloch theorem.
The Kronig Penney model assumes that the crystal lattice is one-dimensional and infinite, the potential is periodic, and there is no interaction between electrons. It also assumes that the electrons are described by a plane wave solution, and that the potential barrier between lattice sites is much smaller than the energy levels of the electrons.
The energy band structure is calculated by solving the Schrödinger equation in reciprocal space, which involves finding the eigenvalues and eigenfunctions of the Hamiltonian matrix. The Hamiltonian matrix is constructed using the periodic potential and the Bloch wave functions, which describe the behavior of the electrons in the crystal lattice.
The Kronig Penney model is used in various fields such as solid state physics, condensed matter physics, and materials science. It helps us understand the electronic properties of crystals, such as their electrical conductivity and optical properties. It is also used in the design and development of electronic devices and materials with specific electronic properties.