Crystal Lattices question to calculate the miller indices, Number of atoms............

Question

Robert · Accepted Answer

Solution: 
a) Number of Atoms per unit cell = 2*0.5 +4*0.25 = 2
Solution: 
a) (1 1 1) 
b) (2 2 1) 
c) (0 1 1) 
d) (1 0 1)
Solution: 
Assume the potential U(x) in the time-independent Schrodinger equation to be zero inside a 
one-dimensional box of length L and infinite outside the box. For a particle inside the box a free 
particle wavefunction is appropriate, but since the probability of finding the particle outside the 
box is zero, the wavefunction must go to zero at the walls. This constrains the form of the 
solution to
and after normalization, the wavefunction is
 
For the particle in a box with infinite walls, the probability must be equal to one for finding it 
within the box. The condition for normalization is then 
 

Boundary Condition: 
Given a potential well as shown and a particle of energy less than the height of the well, the solutions 
may be of either odd or even parity with respect to the center of the well. The Schrodinger 
equation gives trancendental forms for both, so that numerical solution methods must be used.
Solution:

Crystal Lattices question to calculate the miller indices, Number of atoms............

Solution

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