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4604_Exam1_fa06 - PHY4604 Fall 2006 Exam 1 PHY 4604 Exam...

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PHY4604 Fall 2006 Exam 1 Department of Physics Page 1 of 5 PHY 4604 Exam 1 (Total Points = 100) Problem 1 (20 points): Circle true or false for following (2 point each). (a) (True or False) One of the “breakthroughs” that lead to quantum mechanics was the idea of associating differential operators with the dynamical variables. (b) (True or False) Solutions of Schrödinger’s equation of the form ) ( ) ( ) , ( t x t x φ ψ = Ψ correspond to states with definite energy E . (c) (True or False) Solutions of Schrödinger’s equation of the form ) ( ) ( ) , ( t x t x φ ψ = Ψ correspond to states in which the probability density 2 | ) , ( | ) , ( t x t x Ψ = ρ is independent of time. (d) (True or False) The wave function Ψ (x,t) must vanish in a region of infinite potential. (e) (True or False) It is possible for a free particle to have a definite energy. (f) (True or False) In quantum mechanics particles can enter the “classically forbidden” region where V 0 > E ( i.e. KE < 0). (g) (True or False) The operator A op A op is hermitian. (h) (True or False) If A op and B op are hermitian then A op B op is also hermitian. (i) (True or False) The commutator operator [(p x ) op ,(x 2 ) op ] is equal to h i 2 . (j) (True or False) In position-space the commutator operator [(p x ) op ,sin(kx)] is equal to ) cos( kx k i h .
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