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

To find the normalization constant A, we need to use the formula:

$\int_{-\infty}^{\infty} |\psi(x)|^2dx = 1$

Since the particle is confined to −2.00 m ≤ x ≤ +2.00 m, we only need to integrate over this range:

$\int_{-2}^{2} |\psi(x)|^2dx = 1$

Looking at the graph, we can see that the maximum value of $|\psi(x)|^2$ is approximately 0.45. Therefore, we can estimate the integral as:

$\int_{-2}^{2} |\psi(x)|^2dx \approx 0.45 \cdot 4 = 1.8$

To normalize the wave function, the integral must be equal to 1. Therefore, we need to divide the wave function by a constant of:

$A = \sqrt{\frac{1}{1.8}} \approx 0.8341$

The answer choice closest to this value is C: 11eb6adc_eda0_5926_b0cf_812e2c23795a_TB8245_11.

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