hw4 - oscillator. Compare your result with the solution of...

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Assignment #4 PHYS-446 due in class on 10 October 2008 1. (Griffiths, problem 2.42) Find the allowed energies of the half harmonic oscillator V x = { 1 / 2 m 2 x 2 for x 0 for x 0 (This represents, for example, a spring that can be stretched, but not compressed.) Hint: This requires some careful thought, but very little actual computation. 2. Show that [ a + ,a - ]= 1 . 3. Calculate [ p 2 ,x ] . 4. Using the raising and lowering operators, construct the second excited state of the harmonic
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Unformatted text preview: oscillator. Compare your result with the solution of the harmonic oscillator found using the analytic (or brute-force) method. Do you get the same answer? 5. (Griffiths, problem2.12) Find x , p , x 2 , p 2 and T for the n th stationary state of the harmonic oscillator, using the method of Example 2.5. check that the uncertainty principle is satisfied....
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This note was uploaded on 04/11/2010 for the course PHYS 446 taught by Professor Vachon during the Fall '08 term at McGill.

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