Question

(a) A particle of mass $M$ is confined by an infinite potential to a three-dimensional square well of length $Z$. Use the separation of variables technique to show that the eigenfunctions and eigenenergies for the 3D well are given respectively by: $\psi(x, y, z) = A \sin(\frac{n_x \pi x}{L_x}) \sin(\frac{n_y \pi y}{L_y}) \sin(\frac{n_z \pi z}{L_z})$ $E(n_x, n_y, n_z) = (\frac{n_x^2}{L_x^2} + \frac{n_y^2}{L_y^2} + \frac{n_z^2}{L_z^2})\frac{h^2 \pi^2}{2m}$ you can presume that, for the one dimensional well, $\psi(x) = A \sin(\frac{n_x \pi x}{L})$ and $E(n_x) = \frac{n_x^2 h^2 \pi^2}{L_x^2 2m}$ and similarly for the other dimensions.

          (a) A particle of mass $M$ is confined by an infinite potential to a three-dimensional square
well of length $Z$. Use the separation of variables technique to show that the eigenfunctions
and eigenenergies for the 3D well are given respectively by:
$\psi(x, y, z) = A \sin(\frac{n_x \pi x}{L_x}) \sin(\frac{n_y \pi y}{L_y}) \sin(\frac{n_z \pi z}{L_z})$
$E(n_x, n_y, n_z) = (\frac{n_x^2}{L_x^2} + \frac{n_y^2}{L_y^2} + \frac{n_z^2}{L_z^2})\frac{h^2 \pi^2}{2m}$
you can presume that, for the one dimensional well,
$\psi(x) = A \sin(\frac{n_x \pi x}{L})$ and $E(n_x) = \frac{n_x^2 h^2 \pi^2}{L_x^2 2m}$
and similarly for the other dimensions.

(a) A particle of mass M is confined by an infinite potential to a three-dimensional square
well of length Z. Use the separation of variables technique to show that the eigenfunctions
and eigenenergies for the 3D well are given respectively by:
ψ(x, y, z) = A sin((nx π x)/(Lx)) sin((ny π y)/(Ly)) sin((nz π z)/(Lz))
E(nx, ny, nz) = ((nx^2)/(Lx^2) + (ny^2)/(Ly^2) + (nz^2)/(Lz^2))(h^2 π^2)/(2m)
you can presume that, for the one dimensional well,
ψ(x) = A sin((nx π x)/(L)) and E(nx) = (nx^2 h^2 π^2)/(Lx^2 2m)
and similarly for the other dimensions.

Added by Kevin L.

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