(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The parity operator is defined as [tex]P \psi (x) = \psi (-x)[/tex]. Show that [tex]P[/tex] and [tex]p_x[/tex] anti-commute, that is, [tex] \{ P,p_x \} = Pp_x + p_xP = 0 [/tex].

2. Relevant equations

[tex]P \psi (x) = \psi (-x)[/tex]

[tex]p_x = - i \hbar \frac{\partial}{\partial x}[/tex]

3. The attempt at a solution

[tex] \{ P,p_x \} \psi(x) = ( Pp_x + p_xP ) \psi(x) = -i \hbar \left[ P \frac{\partial}{\partial x} \psi (x) + \frac{\partial}{\partial x} [ P \psi (x) ]\right] = -i \hbar \left[ \frac{\partial}{\partial (-x)} \psi (-x) + \frac{\partial}{\partial x} \psi (-x) \right] = -i \hbar \left[ - \frac{\partial}{\partial x} \psi (-x) + \frac{\partial}{\partial x} \psi (-x) \right] = 0 [/tex]

Is it valid to say that [tex] P \frac{\partial}{\partial x} \psi (x) = \frac{\partial}{\partial (-x)} \psi (-x) [/tex] ?

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# Homework Help: Anti-commutation of parity operator

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