I am confused about bound states in QM. My book defines bound states as those in which the particle cannot escape to infinite.
It then gives an example of a potential which is infinite when x is less than 0, -V_0 when x is between 0 and a, and 0 when x >= a.
But then it says that "a particle with mass m is in a bound state in this potential with energy <= 0"
How can this particle possibly be in a bound state when it will have a nonzero probability of being at positive infinity?