Decompose the angular function f(0,4)= 2 sin cos , into a linear combination of spherical harmonics.
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- (AA) ²( ▲ B) ²≥ ½ (i[ÂÂ])² If [ÂÂ]=iñ, and  and represent Hermitian operators corresponding to observable properties, what is the minimum value that AA AB can have? Report your answer as a decimal number with three significant figures.Calculate the number of angles that L can make with the z-axis for an l=3 electron.(a) How many angles can L make with the z -axis for an l = 2 electron? (b) Calculate the value of the smallest angle.
- Provide a written answerThe operator în · ở measures spin in the direction of unit vector f = (nx, Ny, N₂) nx = sin cosp ny = sinesino nz = cose in spherical polar coordinates, and ở = (x, y, z) for Pauli spin matrices. (a) Determine the two eigenvalues of û.o.We have a three dimensional vector space where |P1), |P2) and |23) form a complete orthonormal basis. In this vector space we have two states |a)=5i|1)+3i 2)+(-2+2i) 3) and |B) =4i|1)-5 i) Calculate (a and (B, in terms of the dual basis vectors (y|, (p2|, (P3|. ii) Calculate the inner/scalar products (alB) and (Ba). Show that (8|a) =(a|B)".