what are the limitations imposed on acceptable wave functions?
Answers
Explanation:
For a wave function to be acceptable over a specified interval, it must satisfy the following conditions: (i) The function must be single-valued, (ii) It is to be normalized (It must have a finite value), ... (iv) It has continuous first derivative on the indicated interval
According to Born 's conditions, for a wave front to be accepted over a specialized interval, following conditions must be satisfied
• The function must be single valued.
• It must have a finite value or it must be normalized.
• It has continuous first derivative on the indicated interval.
• The wave function must be square integrable.
The above conditions can be explained as
• The wave function must be single valued . It means for any given values of x and t , there should be a unique value of Ψ(x, t) so there is only a single value for the probability of the system being in a given state.
• It must have a finite value or it must be normalized. If an object is NOT at one point , it's existence is spread out. The particle should be at a point.
• Wave function must be continuous - wave function need to be continuous at boundary because it is required that probability should not change.