Wave function generally obeys the Schrodinger Equation
and is normalizable i.e.
The normalized wave function is then .
Note that doesn’t depend on time (just differentiate under integral).
We call the probability density function,
where is the probability of finding the particle in .
Furthermore, we define the probability current:
It follows that
Superposition
Suppose and are normalizable wave functions.
Then so is .
Inner product
For and define
Also write using Dirac Notation.
Not in Part IB though.