Unformatted text preview: well potential always has one bound eigenvalue, no matter how shallow the binding region. What would the eigenfunction look like if the binding region were very shallow? 2. Why do the lowest eigenvalues and eigenfunctions of an inﬁnite square well provide the best approximation to the corresponding eigenvalues and eigenfunctions of a ﬁnite square well? 3. If the eigenfunctions of a potential have deﬁnite parities, the one of lowest energy always has even parity. Explain why. Enrichment Problem A particle of mass m in an inﬁnite square well has a wavefunction at t = 0 proportional to: sin 3 πx 2 L cos πx 2 L . 1. What is ψ ( x,t ) for t > 0? 2. What are the expectation values of x and p , including time dependence? 1...
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- Spring '09
- mechanics, TA, 2L, Infinite Square, normalized state |n