Consider the square unit cell of identical atoms shown below. The equilibrium separation of atoms is a. In the tight-binding model of this system find the Hamiltonian of an electron ) assuming the hopping parameter in x and y directions is t. ID assuming the hopping parameter in x (y) direction is t. (ty). Find the general expression, and then calculate it for t = t = 2ty .

Can you solve only B

What will happen if we put a spin-1 particle inside the 3D potentialwell? Find out the density of states for the system.

Prove the angular momentum of a single electron..

P9E.11 (a) For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2p orbital, the energies E, of the resulting A molecular orbitals are given by: E, =a+2B cos- N+1 k=1, 2,.,N Use this expression to make a reasonable empirical estimate of the resonance integral B for the homologous series consisting of ethene, butadiene, hexatriene, and octatetraene given that t-n ultraviolet absorptions from the HOMO to the LUMO occur at 61 500, 46 080, 39 750, and 32 900 cm", respectively. (b) Calculate the T-electron delocalization energy, Egdo:= E, - n(a+ B), of octatetraene, where E, is the total T-electron binding energy and n is the total number of T-electrons. (c) In the context of this Hückel model, the molecular orbitals are written as linear combinations of the carbon 2p orbitals. The coefficient of the jth atomic orbital in the kth molecular orbital is given by: cN sin j=1,2.N jkn j=1, 2,.,N Evaluate the coefficients of each of the six 2p orbitals in each…

pls send me answer of this question in written form with expalantion and i will give you like sure Draw the projections for spin angular momentum. Calculate the angles between the z-axis and the spin angular momentum S of the electron in the up and down spin states.

Write down the confi gurations for the ground states of calcium and aluminum. What are the LS coupling quantum numbers for the outside subshell electrons? Write the spectroscopic symbol for each atom

The Hamiltonian of a spin S in a magnetic field B is given by \hspace {3cm} H = -yS · B where y is a positive constant. If a magnetic field of strength B is applied in the z– direction for a spin-half single electron system, taking @ = y B, the eigenvalues of the Hamiltonian are Select one: a. -ho, ħo O b. -hw,0, ¿ħo -ho, ho Ос. O d. -ho, ho O e. -ħw, 0, ħo

a) Explain how the alpha parameter in the general E(p) relation, and the channel dimension could be used to determine the density of states as function of the energy E.        b) Provide and define the two main parameters (terms) that determine the electron density when temperature is non zero.