- #1
Mithra
- 16
- 0
Hi there, I apologise that I should probably know this/its a stupid question but I seem to have forgotten all physics over the holiday and so any help would be great!
I have been told that there is a beam of atoms with spin quantum number 1/2 and zero orbital angular momentum, with spin +1/2 along the x axis. I am then asked what the spin state function of this beam is in terms of eigenfunctions of [itex]\hat{S}^2[/itex] and [itex]\hat{S}_z[/itex], being the kets |[itex]1/2 , m_{s_z} = 1/2>[/itex] and |[itex]1/2 , m_{s_z} = -1/2>[/itex]
Would I be right in assuming that the answer is simply
[itex]\phi_s = \frac{1}{\sqrt{2}}|1/2 , m_{s_z} = 1/2> + \frac{1}{\sqrt{2}}|1/2 , m_{s_z} = 1/2> [/itex]
because knowing the spin in the x direction doesn't tell you about the z direction (as they are incompatible observables) or is it more complex than that? Any help/advice greatly appreciated, thanks.
I have been told that there is a beam of atoms with spin quantum number 1/2 and zero orbital angular momentum, with spin +1/2 along the x axis. I am then asked what the spin state function of this beam is in terms of eigenfunctions of [itex]\hat{S}^2[/itex] and [itex]\hat{S}_z[/itex], being the kets |[itex]1/2 , m_{s_z} = 1/2>[/itex] and |[itex]1/2 , m_{s_z} = -1/2>[/itex]
Would I be right in assuming that the answer is simply
[itex]\phi_s = \frac{1}{\sqrt{2}}|1/2 , m_{s_z} = 1/2> + \frac{1}{\sqrt{2}}|1/2 , m_{s_z} = 1/2> [/itex]
because knowing the spin in the x direction doesn't tell you about the z direction (as they are incompatible observables) or is it more complex than that? Any help/advice greatly appreciated, thanks.