Prove the relationship [x,px]=ih, where px =-ihd/dx. Namely, show that applying the commutator [x,px] to any function f(x) is equal to multiplying ih to f(x).© BrainMass Inc. brainmass.com October 24, 2018, 5:32 pm ad1c9bdddf
[A,B] = A B - B A
[x,px] = x px - px x = x(-ihd/dx) - (-ihd/dx)x
= -ih x ...
The expert proves the relation of a function. The commutator function is applied. The solution is given in a step-by-step equational process.
Octahedral Distortion to D2d and D2h
The octahedra of anatase and rutile TiO2 both have elongation along the z-axis (apical). Anatase experiences more angular distortion around the equatorial bonds. Why is anatase classified as D2d (meaning the dz^2, dxz and dyz states have an INCREASE in energy), while rutile is D2h (meaning these states have LOWER energy), if both have elongation along the z-axis and should therefore both have reduced repulsion between the central cation and the ligands?
A thought is that the angular distortion of the equatorial ligands somehow stabilizes the d orbitals with only xy components, but I don't know why these components would be more stabilized than those with z components, since the elongation along z should lower the repulsion.View Full Posting Details