Uncertainty Principle
and
a particle in a Box

Define the wave function

a). - Calculate < x> and <>

b). - Calculate < p> and <>

Notice that Cos[2 n π] is equal to + 1 or -1 depending on n being  even or odd.  But the Cos function is squared

c). - Calculate Δx Δp

Consider the following function

The minum value of f is f[1]

Therefore
delx  delp >=