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Unformatted text preview: Quantum Mechanics Problem Sheet 5 (These problems will be discussed in the practice session on Friday, 17 Feb 2006) 1. Consider a particle bound in a finite square well V ( x ) = - V for- L 2 < x < L 2 , for | x | > L 2 . (a) Solve the stationary Schr¨ odinger equation for- V < E < 0 and consider only odd-parity solutions, ie those for which φ ( x ) =- φ (- x ) . Work with the abbreviations κ ≡ √- 2 mE/ ¯ h and k ≡ p 2 m ( E + V ) / ¯ h , as we did in the lectures. (b) Sketch the form of the lowest-energy odd-parity wave function φ ( x ). (c) Using the continuity conditions on φ ( x ) and d φ/ d x , show that y =- z cot z y 2 + z 2 = R 2 , where z ≡ kL/ 2, y ≡ κL/ 2, and R ≡ √ 2 mV L/ (2¯ h ). (Because of the symmetry of the wave function you need to consider the continuity conditions only at x =- L/ 2 or at x = L/ 2 , but not both. If you consider them at both points you just get twice the same equation.) (d) Sketch the solution for ( y, z ) and determine the number of odd-parity bound states for the case...
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This note was uploaded on 04/07/2008 for the course PHYS F3026 taught by Professor Eberlein during the Spring '06 term at Uni. Sussex.
- Spring '06