ps5 - Quantum Mechanics Problem Sheet 5(These problems will...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 2

ps5 - Quantum Mechanics Problem Sheet 5(These problems will...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online