(a) Cite a Hamiltonian from Chapter 2 (other than the harmonic oscillator) that has only a discrete spectrum.
(b) Cite a Hamiltonian from Chapter 2 (other than the free particle) that has only a continuous spectrum.
(c) Cite a Hamiltonian from Chapter 2 (other than the finite square well) that has both a discrete and a continuous part to its spectrum.
(a) Infinite square well (Eq. 2.22).
V(x)= \begin{cases}0, & 0 \leq x \leq a \\ \infty, & \text { otherwise }\end{cases} (2.22).
(b) Delta-function barrier (Fig. 2.15), or the finite rectangular barrier (Prob. 2.33).
(c) Delta-function well (Eq. 2.114), or the finite square well (Eq. 2.148) or the \text { sech }^{2} potential (Prob. 2.52).
\delta(x) \equiv\left\{\begin{array}{ll} 0, & \text { if } x \neq 0 \\ \infty, & \text { if } x=0 \end{array}\right\}, \text { with } \int_{-\infty}^{+\infty} \delta(x) d x=1 (2.114).
V(x)= \begin{cases}-V_{0}, & -a \leq x \leq a \\ 0, & |x|>a\end{cases} (2.148).
