Is the given 1-D potential an example of a bound state?

[dyn]

In 1-D if I have an infinite potential at x<0 so the wavefunction is zero for x<0 but for x>0 the potential is zero so the wavefunction oscillates to infinity is that a bound state ? I presume this isn't bound as it can't be normalized but most definitions state that bound means the wavefunction tends to zero as x tends to + or - infinity. so is my example bound ? Thanks

 

[ShayanJ]

No, its not bound because it can radiate to infinity. See here!