The graph below represents a wave function ψ(x)for a particle confined to −2.00 m ≤ x ≤ +2.00 m.The value of the normalization constant A may be
A) .
B) .
C) .
D) .
E)either or .

Question

The graph below represents a wave function ψ(x)for a particle confined to −2.00 m ≤ x ≤ +2.00 m.The value of the normalization constant A may be 
A) . 
B) . 
C) . 
D) . 
E)either or .

Quizplus · Accepted Answer

For a wave function to be normalized, the integral of the absolute value squared of the wave function over all space must equal 1.
So, we need to calculate the integral of |ψ(x)|^2 over the given interval:
∫[from -2 to 2] |ψ(x)|^2 dx = A^2 * ∫[from -2 to 2] (4 - x^2)^2 dx
= A^2 * ∫[from -2 to 2] (16 - 8x^2 + x^4) dx
= A^2 * [128/15]
To normalize the wave function, this integral must equal 1.
Therefore, A^2 * [128/15] = 1
A^2 = 15/128
A = sqrt(15/128) = 11ea7ff9_2c68_2bd9_a768_79dd78c54a65_TB2295_11 (in scientific notation)

The Graph Below Represents a Wave Function ψ(X)for a Particle