Question

Consider the wavefunction 𝜓(𝑥) = 𝑁[exp(𝑖𝑘𝑥) + exp(−𝑖𝑘𝑥)]. The complex conjugate 𝜓 ∗ (𝑥) is [Given: 𝑁 is the normalization constant; 𝑖=\(\sqrt-1\)]

• A. 𝑁[exp(−𝑖𝑘𝑥) − exp(𝑖𝑘𝑥)]
• B. 𝑁∗[exp(−𝑖𝑘𝑥) − exp(𝑖𝑘𝑥)]
• C. 𝑁∗[exp(𝑖𝑘𝑥) + exp(−𝑖𝑘𝑥)]
• D. 2𝑁[sin(𝑘𝑥)]

Answer 1

The Correct Option is C

• The complex conjugate ψ∗(x) is obtained by replacing i with −i and taking the conjugate of the normalization constant N, resulting in N∗.
• Applying this to ψ(x) = N[exp(ikx) +exp(−ikx)]:

  \( ψ^*(x) = N^*[\exp(-ikx) + \exp(ikx)] \)

  \( = N^*[\exp(ikx) + \exp(-ikx)]. \)

Thus, the correct expression for the complex conjugate is \(N^*[\exp(ikx) + \exp(-ikx)].\)