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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 mo-tion 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 quantum-mechanical wave function is the coherent-state wave function deFned in (a). This is why the coherent state is sometimes called the quasi-classical state. (d). Not to be turned in. Show that in the coherent state, the expec-tation 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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