Question

A particle of mass $m$ with no spin is confined inside a rectangular box with sides $a$, $b$, and $c$. The eigen-functions of this particle are given by \begin{equation} \Psi_{n_x, n_y, n_z}(x, y, z) = \sqrt{\frac{8}{abc}} \sin\left(\frac{n_x \pi}{a} x\right) \sin\left(\frac{n_y \pi}{b} y\right) \sin\left(\frac{n_z \pi}{c} z\right), \end{equation}where $n_x, n_y, n_z = 1, 2, 3, \dots$ Find the parity of these states. Remember that the parity operator acts on a function as \begin{equation} P\Psi_{n_x, n_y, n_z}(r, \theta, \phi) = \Psi_{n_x, n_y, n_z}(r, \pi - \theta, \pi + \phi). \end{equation}

          A particle of mass $m$ with no spin is confined inside a rectangular box with sides $a$, $b$, and $c$. The eigen-functions of this particle are given by
\begin{equation}
\Psi_{n_x, n_y, n_z}(x, y, z) = \sqrt{\frac{8}{abc}} \sin\left(\frac{n_x \pi}{a} x\right) \sin\left(\frac{n_y \pi}{b} y\right) \sin\left(\frac{n_z \pi}{c} z\right),
\end{equation}where $n_x, n_y, n_z = 1, 2, 3, \dots$ Find the parity of these states.
Remember that the parity operator acts on a function as
\begin{equation}
P\Psi_{n_x, n_y, n_z}(r, \theta, \phi) = \Psi_{n_x, n_y, n_z}(r, \pi - \theta, \pi + \phi).
\end{equation}

A particle of mass m with no spin is confined inside a rectangular box with sides a, b, and c. The eigen-functions of this particle are given by

Ψnx, ny, nz(x, y, z) = √((8)/(abc))sin((nx π)/(a) x) sin((ny π)/(b) y) sin((nz π)/(c) z),
where nx, ny, nz = 1, 2, 3, … Find the parity of these states.
Remember that the parity operator acts on a function as

PΨnx, ny, nz(r, θ, ϕ) = Ψnx, ny, nz(r, π - θ, π + ϕ).

Added by Julia A.

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