next up [*]
Next: 4.3 Some consequences Up: 4. Bound states of Previous: 4.1 B2 = 0

4.2 A2 = 0

In this case A1 = - B3, and the relation between k and $ \kappa$ is modified to

ka = - $\displaystyle \kappa$acot$\displaystyle \kappa$a. (4.18)

From the graphical solution, in Fig. 4.3 we see that this type of solution only occurs for $ \kappa_{0}^{}$a greater than $ \pi$/2.

  
Figure 4.3: The graphical solution for the odd states of the square well.
\includegraphics[width=10cm]{Figures/sq_well_odd.ps}

In the middle region all these solutions behave like sines, and you will be asked to show that the solutions turn into minus themselves when x goes to - x. (We say that these functions are odd.)

© 1998 Niels Walet, UMIST
Email Niels.Walet@umist.ac.uk