Parity
Tags: #physics #quantumEquation
$${\cal P}\psi(x)=\psi(-x) \\ \psi(x)= \underbrace{\frac{1}{2} (\psi(x)+\psi(-x))}_{\rm even:~\hbox{$\psi^+$}}+ \underbrace{\frac{1}{2} (\psi(x)-\psi(-x))}_{\rm odd:~\hbox{$\psi^-$}} \\ \psi^+= \frac{1}{2} (1+{\cal P})\psi(x,t) \\ \psi^-= \frac{1}{2} (1-{\cal P})\psi(x,t)$$Latex Code
{\cal P}\psi(x)=\psi(-x) \\
\psi(x)= \underbrace{\frac{1}{2} (\psi(x)+\psi(-x))}_{\rm even:~\hbox{$\psi^+$}}+ \underbrace{\frac{1}{2} (\psi(x)-\psi(-x))}_{\rm odd:~\hbox{$\psi^-$}} \\
\psi^+= \frac{1}{2} (1+{\cal P})\psi(x,t) \\
\psi^-= \frac{1}{2} (1-{\cal P})\psi(x,t)
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Introduction
Equation
Latex Code
{\cal P}\psi(x)=\psi(-x) \\
\psi(x)= \underbrace{\frac{1}{2} (\psi(x)+\psi(-x))}_{\rm even:~\hbox{$\psi^+$}}+ \underbrace{\frac{1}{2} (\psi(x)-\psi(-x))}_{\rm odd:~\hbox{$\psi^-$}} \\
\psi^+= \frac{1}{2} (1+{\cal P})\psi(x,t) \\
\psi^-= \frac{1}{2} (1-{\cal P})\psi(x,t)
Explanation
Latex code for the Parity Equation. If the wavefunction is split into even and odd functions, it can be expanded into eigenfunctions of P. I will briefly introduce the notations in this formulation.
: parity operator
: Even Function
: Odd Function
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