Quantum Energy of a Nanoparticle in Superposition Two States on R2

Abstract

Papa M Seck and Dereje Seifu

We explore the probability distribution of a nanoparticle through the two-state linear combination wave function system. A mathe- matical function represents the superposition wave function of the particle, in which the potential energy is described in (R2 ). This is typically done in an infinite rectangular well function where we define the boundary condition states of the nanoparticle moving between the two walls. We perform an eigenstate energy analysis using a time-dependent Schrödinger equation of a Hamiltonian operation wavefunction. We use computer programming to determine the energy of the nanoparticle given by E =< Ψ|H|Ψ >, the probability of finding the two states |Ψ(x,y,t)|2 . It will be carried out within the framework density functional theory by solving the Kohn-Sham equation with a spin-polarized calculation, where the density of nanoparticles is calculated for the spin-up ↑ and spin- down ↓ structure [1,2]. The result shows that the quantum superposition of the expected energy of the two states changes with the sinusoidal function of the energy levels of the eigenvalues, which means that the energy will oscillate between higher and lower values when the relative phase between the two states changes.

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