Proving Parity in Normalized Solutions of the Schrodinger Equation

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The discussion focuses on demonstrating that normalized solutions to the time-independent Schrödinger equation exhibit definite parity when the potential V(x) is even, meaning V(x) = V(-x). The user is struggling to prove that the solutions satisfy the condition u(x) = ±u(-x). They attempted to substitute y = -x into the equation but found their approach unconvincing and did not achieve a clear solution. The user seeks guidance on how to effectively normalize their findings and establish the parity of the solutions. Overall, the thread highlights the challenge of proving parity in quantum mechanics under specific potential conditions.
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Hopefully this is in the correct section.

Struggling with this question though I don't think it should be particularly difficult:

Show that if V(x) = V(-x) normalised solutions to the time-independent Schrodinger equation have definite parity - that is, u(x) = +-u(-x)

(+- means plus or minus. Sorry for poor formatting - on phone)

Thanks in advance.
 
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Just read the "how to ask for help" sticky.

My attempt at a solution involved subbing y = -x. Obtaining a solution, then trying to normalise it. However I don't get anywhere really, and my line of argument through my current page of working reads unconvincing (I'm just guessing).

Cheers
 

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