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Show for stationary eigenstates of the Schrodinger equation in one dimension. When the potential has inversion...

Show for stationary eigenstates of the Schrodinger equation in one dimension.

When the potential has inversion symmetry, V (x) = V (−x), parity is conserved in bound states: the eigenfunction is either even (ψ(x) = ψ(−x)) or odd (ψ(x) = −ψ(−x)) under parity transformation, x → −x.

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