3 14 19 30 46 51 Q1:- Work out the following commutation relations [z, P], [z,...

  

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3 14 19 30 46 51 Q1:- Work out the following commutation relations [z³, P₂], [z, H], [a,H] Q2:- construct the Y₂¹(0, 0), Y¹ (0,), check they are normalized and orthogonal Q3:- Use the equation(Q)=([1.Q]+) dv to show that <P₂ >=< dz Q4:- for Harmonic oscillator obtain normalized , ₁, check they are orthogonal? Q5:-:-Consider a particle in an infinite square well whose wave function is given by 0<x<a p(x) = [Ax(a-x²) otherwise 1- Is this acceptable wave function 2- Find A 3- Calculate the position and momentum uncertainty 16m²h² 4 Calculate the probability of finding- 2ma² 35 3 14 19 30 46 51 Q1:- Work out the following commutation relations [z³, P₂], [z, H], [a,H] Q2:- construct the Y₂¹(0, 0), Y¹ (0,), check they are normalized and orthogonal Q3:- Use the equation(Q)=([1.Q]+) dv to show that <P₂ >=< dz Q4:- for Harmonic oscillator obtain normalized , ₁, check they are orthogonal? Q5:-:-Consider a particle in an infinite square well whose wave function is given by 0<x<a p(x) = [Ax(a-x²) otherwise 1- Is this acceptable wave function 2- Find A 3- Calculate the position and momentum uncertainty 16m²h² 4 Calculate the probability of finding- 2ma² 35