I discussed in the previous chapter you the probability of a particle being detected in the continous range can be calculated from its wavefunction using,
Now, assuming the particle actually exists, if we essentially look for it at every point in the entire universe we’re bound the detect it somewhere right? Hence the probability of finding the particle in the range should be . In other words,
- must equal .
So, what if we get a wavefunction, say. where doesn’t equal and equals some other number instead? Then we can make the function’s probability equal bu multiplying it with a constant , such that the corrected wavefunction is:
This process is called normalizing the wavefunction. But how do we figure out what the value of is? Notice that now that ,
Now we already know that , so the above expression simplifies to:
Now to ensure , we need a value for such that