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Two wave functions \(\psi_m(x)\) and \(\psi_n(x)\) are said to be orthogonal if

Question and options

Two wave functions ψm(x)\psi_m(x) and ψn(x)\psi_n(x) are said to be orthogonal if
  1. ∫ψm(x) ψn(x) dx=0\int \psi_m(x)\,\psi_n(x)\,dx = 0
  2. ∫ψm∗(x) ψn(x) dx=0\int \psi_m^*(x)\,\psi_n(x)\,dx = 0
  3. ∫ψm(x) ψn(x) dx=1\int \psi_m(x)\,\psi_n(x)\,dx = 1
  4. ∫ψm∗(x) ψn(x) dx=1\int \psi_m^*(x)\,\psi_n(x)\,dx = 1

Answer and explanation

Correct answer: B - \(\int \psi_m^*(x)\,\psi_n(x)\,dx = 0\)
Orthogonality of (generally complex) wave functions is defined as ∫ψm∗ψn dx=0\int \psi_m^*\psi_n\,dx = 0 for m≠nm \neq n; =1= 1 would be normalisation.

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