Let us consider an asymmetric potential, which is piecewise defined as $V_1$ for $x<0$, $0$ when $0<x<a$ and $V_2$ for $x>a$, together with the condition $V_1 > V_2 >0$.
In the first region, the wavefunction will be oscillatory, while in the middle region, it will display an exponential decay. In the third region it will oscillate again but with decreased amplitude.
In order to find out the discrete energy levels of this setup, does $E$ need to be greater or less than the potential?
I think the former is known as an unbound state and the latter as a bound state? Can states with discrete energy levels be found for either case?