hw3 - H . How does it compare with E 1 and E 2 ? 3....

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Assignment #3 PHYS-446 due in class on 3 October 2008 1. A particle is confined to an infinite square well defined as V x = { V 0 0 x 2a otherwise where V 0 and a are positive real constants. Calculate the general wave function x ,t of a particle stuck in this well. 2. A particle in the infinite square well has as its initial wave function an even mixture of the first two stationary states:  x , 0 = A [ 1 x  2 x ] (a) Normalize  x , 0 .(That is, find A. Hint : There's a shortcut if you exploit the orthonormality of 1 and 2 ) (b) Find  x ,t and ∣ x ,t ∣ 2 . (c) If you measured the energy of this particle, what values might you get, and what is the probability of getting each of them? (d) Find the expectation value of
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Unformatted text preview: H . How does it compare with E 1 and E 2 ? 3. (Griffiths, Problem 2.38) A particle of mass m is in the ground state of the infinite square well. Suddenly the well expands to twice its original size the right wall moving from a to 2 a leaving the wave function (momentarily, or if you prefer, instantaneously) undisturbed. The energy of the particle is now measured. (a) What is the most probable result? What is the probability of getting that result? (b) What is the next most probable result, and what is its probability? (c) What is the expectation value of the energy? Hint: If you find yourself confronted with an infinite series, try another method....
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