Find the normalization constant for the wave function (e^-bx).(e^+bx)(one dimension)
To find the normalization constant for the given wave function, we need to calculate the integral of the absolute square of the wave function and then find the value that makes the integral equal to 1.
The given wave function is:
Ψ(x) = (e^-bx).(e^+bx)
To normalize it, we need to square the wave function to get the absolute square:
|Ψ(x)|^2 = Ψ(x) * Ψ*(x)
= (e^-bx).(e^+bx) * (e^-bx).(e^+bx)
= e^-bx * e^+bx * e^-bx * e^+bx
= e^0
= 1
Since the squaring of the wave function resulted in a constant value of 1, we can say that the wave function is already normalized. Therefore, the normalization constant is equal to 1.