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Unformatted text preview: 2. What is the expectation value? What is the general expression for the expectation value of an operator? 3. A large part of quantum mechanics is devoted to the study of the solutions of the Schroedinger equation for diﬀerent potentials. What are the forms of the potential for the following: (a) a free particle (b) a particle in a box of length a (c) a harmonic oscillator 4. What are the conditions that the wavefunction must satisfy for the particle in a box problem? 1 Enrichment Problem Consider a system with potential energy given by: V ( x ) = 1 2 mω 2 x 2 1. What kind of potential is this? 2. What does it mean for a function to be an eigenfunction of a system? 3. Show that: φ = Aeαx 2 is an eigenfunction of this system for a particular value of α . What is the value? 4. What is the value of the energy E for this eigenfunction? 2...
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 Spring '09
 mechanics, expectation value, Matter wave, infinite potential wells, probability maxima

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