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Unformatted text preview: a = i A a a . (4) Solve this equation for A a a ( t ) in terms of A a a (0). 1 (c). According to Shankar, eq. (7.4.3), a a A = r m/ (2 h ) a X A + i r 1 / (2 m h ) a P A . Now, consider the classical harmonic oscillator, whose equation of motion is just x = ( k/m ) x, (5) where k/m = 2 . By solving for the classical x ( t ) and p ( t ) , show that a X A ( t ) and a P A ( t ) reduce to the classical solutions if the quantummechanical wave function is the coherentstate wave function deFned in (a). This is why the coherent state is sometimes called the quasiclassical state. (d). Not to be turned in. Show that in the coherent state, the expectation value of the commutator X P is the minimum value allowed by the Heisenberg uncertainty principle. 2. (10pts.) Shankar, exercise 10.2.2. 3. (10pts.) Shankar, exercise 10.2.3. 2...
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 Fall '07
 STROUD
 Physics, mechanics

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