hw6 - Chemistry 550 / 475 Homework Assignment #6 due:...

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Chemistry 550 / 475 – Homework Assignment #6 due: Friday, November 4th at 5:00 pm Readings : Chapters 5 and 6 in Levine Problem 1 - Warm up. For the state represented by the wave function ψ ( x ) = N e αr 2 ( x + y ) z with r = | x | = r x 2 + y 2 + z 2 a. determine the normalization constant N as a function of the parameter α. b. calculate the expectation values of the operators L = x × p and L 2 = L · L . c. calculate the variances of these quantities in ψ . Problem 2 - Hydrogen atom. Based upon our knowledge of the postulates of quantum mechanics we know that two Hermitian operators commute if and only if they share a common complete set of eigenfunctions. a. Compute the commutators of the angular momentum operator L with its square, [ L , L 2 ] . Also compute the commutators of all possible angular momentum components (i.e., x , y , and z components) among themselves. In light of your answers what can be said about the eigenstates of L and L 2 ? b.
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hw6 - Chemistry 550 / 475 Homework Assignment #6 due:...

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