My question is quite simple. Suppose we are given a potential such as a potential barrier (potential $V = V_0, -a \leq x \leq a$ and 0 otherwise). Will scattering states which are solutions to this potential exhibit definite parity ($\psi(x) = \pm\psi(-x)$)?
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Qmechanic
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Related/possible duplicate: https://physics.stackexchange.com/q/112553/50583 – ACuriousMind Oct 05 '21 at 15:25
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Related: https://physics.stackexchange.com/q/13980/2451 – Qmechanic Oct 05 '21 at 18:30
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I did not feel that this was a duplicate since the question you have linked to talks about bound states whereas my question relates to scattering states – Siddharth Yajaman Oct 08 '21 at 08:39
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Yeah, Of course! Since $$V(x)=V(-x)\rightarrow \psi(x)=\pm \psi(-x)$$
Young Kindaichi
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2Can you prove this implication? In general, symmetries of the action/Lagrangian/potential do not need to be symmetries of the solutions to the equations of motion! – ACuriousMind Oct 05 '21 at 15:23