The wave function shown in Fig. 40.20 is nonzero for both x < 0 and x > L. Does this mean that the particle splits into two parts when it strikes the barrier, with one part tunneling through the barrier and the other part bouncing off the barrier? Explain.

Fig.40.20

The wave function is exponential within the barrier (0 sxs L). U(x) Uo Mx) L. and sinusoidal outside the barrier. The function and its derivative (slope) are continuous at x = 0 and x = L, so the sinusoidal and exponential functions join smoothly.