3.4.1 Commuting operators

1

What does it mean if two operators $A$ and $B$ commute?

2

Commute or don't commute?

• Particle in a box: $H_x$ and $H_y$? $H$ and $H_x$?
• Harmonic oscillator: $H_x$ and $H_y$? $H$ and $H_x$?
• Hydrogen atom: $H$ and $\L ^2$? $H$ and $\L _z$? $H$ and $\L _x$? $\L ^2$ and $\L _z$? $\L ^2$ and $\L _x$? $\L _z$ and $\L _x$?
• Generic particle: ${\widehat x}$ and ${\widehat p}_x$? ${\widehat x}$ and $p_z$?