Contemporary Examples. 1  dangle mere feet from one of these behemoths to feel very small indeed. 2  And, like it or not, those are exactly the types of players at whom the Yankees like to dangle money, yearly. 3  Plenty of novels can dangle the facts well enough to merit our page-turning interest.
Bloch theorem. A theorem that specifies the form of the wave functions that characterize electron energy levels in a periodic crystal. Electrons that move in a constant potential, that is, a potential independent of the position r, have wave functions that are plane waves, having the form exp(i k Â· r).he theorem that the lowest state of a quantum-mechanical system without a magnetic field can carry no current. (solid-state physics). The theorem that, in a periodic structure, every electronic wave function can be represented by a Bloch function.
The ï¬nal solutions for each k are therefore (this is anotherstatement of Blochâs theorem):Ï k (r) = X G C k+G e ik+GÂ·r /ââ¦for a Hamiltonian H k+G,k+G 0 = H GG (k) = Î´ GG 0 (k+G) 2 /2m+VË GâG.Notethat Ï k has the additional property of being periodic in the reciprocal space:Ï k (r) = Ï k+G (r).n the following,we will ï¬rst introduce and prove Blochâs theorem which is based on thetranslational invariance of the system; then make use of it to simplify thediï¬cult task of ï¬nding the eigenstates and eigenvalues of the inï¬nite crystalHamiltonian.1.