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

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SUMMARY

The discussion centers on the classification of a 1-D potential with an infinite barrier at x<0 and zero potential for x>0. The consensus is that this scenario does not represent a bound state, as the wavefunction oscillates to infinity and cannot be normalized. According to established definitions, a bound state requires the wavefunction to approach zero as x approaches both positive and negative infinity, which is not satisfied in this case.

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

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