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Quiz 3 Chem 3730 January 29, 2006 Answer all the questions below in the space provided. You may use maple to aid in your analysis. 1) The kinetic energy for a particle moving in three dimensions is determined using the operator: p 2x p 2y p 2z K 2m The angular momentum operator is given by: ˆ yp zp ˆi xp zp ˆj xp yp kˆ L z y z x y x Therefore the x component is given by: ˆ yp zp L x z y a) Determine whether K commutes with Lx which is the x operator. (5 marks) b) Using the above results comment on whether similar behavior is expected for Ly and Lz and argue either that L commutes with K or not. (2marks) 2) A modified from of the 1D particle in the box equation ranging over 0 < x < 1 is given as: ( x) sin 5 x exp 5( x 0.5) 2 a) This wave equation is not normalized. Determine the normalization constant and state the normalized form of the wave function. (show work) (Hint: the expression looks a bit complicated. Don’t be intimidated! Just determine the value using the evalf command). (5 marks) See Maple file quiz3-2006 b) Plot and sketch the probability distribution of the particle as a function of x. (3 marks) c) Determine the probability of finding the particle between 3/5 and 4/5. (5marks) (show work)