This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: PHY4604 Exam 2 Solutions Department of Physics Page 1 of 9 PHY 4604 Exam 2 Solutions (Total Points = 100) Problem 1 (20 points) Problem 1a (2 points): The wave function for an electron in a state with zero angular momentum: ( circle the correct answer ) (a) is zero everywhere (b) is spherically symmetric (c) depends on the angle from the z axis (d) depends on the angle from the x axis (e) is spherically symmetric for some shells and depends on the angle from the z axis for others Problem 1b (2 points): The magnitude of the orbital angular momentum of an electron in an atom is what multiple of h ? ( l = 0, 1, 2, ) ( circle the correct answer ) (a) 1 (b) (c) ) 1 ( + l l (d) 1 2 + l (e) 2 l Problem 1c (2 points): An electron is in a quantum state for which the magnitude of the orbital momentum is h 2 6 . How many allowed values of the zcomponent of the angular momentum are there? ( circle the correct answer ) (a) 4 (b) 5 (c) 7 (d) 8 (e) 9 I goofed up this problem. The correct answer is 17. Problem 1d (2 points): If the wave function is spherically symmetric then the radial probability density is given by: ( circle the correct answer ) (a) 2 4 r (b) 2   (c) 2 2   4 r (d) 2   4 (e) 2   4 r Problem 1e (3 points): An electron in an atom is in a state with l = 3 and m l = 2 . The angle between L r and the zaxis is given by: ( circle the correct answer ) (a) 48.2 (b) 60 (c) 30 (d) 35.3 (e) 54.7 Problem 1f (3 points): SU(2) is the group of 22 matrices, U , where: (a) 1 = = UU U U (b) = U U (c) det(U)=1 (d) = U U 1 (e) T U U = * (Note: circle all the correct answers) Problem 1g (3 points): If H is an Hermitian operator then: (a) 1 = = HH H H (b) = H H (c) <H> 0 (c) <H 2 > 0 (e) its eigenvalues are real (Note: circle all the correct answers) Problem 1h (3 points): If L v is the orbital angular momentum operator then: (a) = y x L L (b)   2 > < z y x L L L h (c) 2 h y x L L (d) 2 L L z (Note: circle all the correct answers) PHY4604 Exam 2 Solutions Department of Physics Page 2 of 9 Problem 2 (30 points): Consider a spin system described by the Hamiltonian: = 1 1 i i H where and 1 are real positive constants. (a) (6 points) Find the energy levels of the sustem. How many energy levels are there? What is the ground state energy, E , and the first excited state energy, E 1 ? Answer: There are two energy levels: E = 1 , E 1 = + 1 . Solution: The energy levels are the solution of 1 1 = i i which yields ) ( 2 1 2 = , which implies that 1 = and hence 1 = . There are two energy levels, E = 1 and E 1 = + 1 ....
View Full
Document
 Spring '07
 FIELDS
 mechanics, Momentum

Click to edit the document details