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Applications of the Formalism-I
Published in Shabnam Siddiqui, Quantum Mechanics, 2018
Thus, the wave function is not normalizable. The wave function of the particle is not physically realizable, but this does not mean that the wave function of the particle is meaningless. To make sense of the wave function, the position space wave function is expressed in its momentum space wave function form, as is shown next. Any position-space wave function is related to its momentum-space wave function form by the following equation which is an inverse Fourier transform of the momentum space wave function to the position space wave function. Ψ(x,t)=12π∫−∞∞∅(k)ei(kx−Etℏ)dk
Applications of Graphene
Published in Andre U. Sokolnikov, Graphene for Defense and Security, 2017
In the central region of Fig. 9.23, EF (the Fermi level) is close to the Dirac point. The Dirac points represent size locations in momentum space. The points are situated on the edge of the Brillouin zone and are being divided into two non-equilibrium sets of three points each. Momentum space, in its turn, is the set of all momentum vectors p that a physical system can possess. The momentum vector of a particle, included in the above system, is characterized by its motion, [mass][length][time]−1. The interband transition causes abruption. If high voltages are applied the Fermi level is at such position that interband transitions are not possible.
Sommerfeld Free Electron Fermi Gas Model
Published in Vinod Kumar Khanna, Introductory Nanoelectronics, 2020
These points are plotted in a three-dimensional space. Three mutually perpendicular axes kx, ky, and kz are chosen. This choice of axes forms a k-space. As the momentum p = ℏk, this space is often referred to as the momentum space. In the ground state, a system of N electrons at 0 K occupies states that have lowest possible energies. As the states are filled with electrons according to the rules for fermions, the energy levels with lowest energies are first filled and this filling moves toward higher energies. The last available state is filled with the electron having the highest energy.
The effect of in-doping on the quantum information entropy of hydrogenic impurity states in the InxGa1-xN semiconductor quantum dot
Published in Philosophical Magazine, 2023
Xue Liu, Xin-yu Xie, De-hua Wang, Chen-lu Wang, Yu-lin Zhao, Shu-fang Zhang
After obtaining the wave function in the position space, we can further derive the wave function in the momentum space. By a spherical Bessel transform of the radial wave function in the position space using Mathematica software, we get [36]: