- #1
member 545369
Hello
In our Quantum Mechanics lecture we have been discussing a simplified model of the Stern-Gerlach experiment. Let ##|+>## and ##|->## denote an electron that is "spin up" and "spin down" (with respect to ##\hat{z}##), respectively. Our professor then asserted that ##|+>## and ##|->## acted as a basis for a 2-D Hilbert space. It follows that a spin in ##\hat{x}## could then be constructed in the following way: $$|+_x > = \frac{1}{\sqrt{2}} ( |+> + |->)$$ however, this confuses me. How can we possible construct a ket pointing in ##\hat{x}## out of kets pointing in ##\hat{z}##??
In our Quantum Mechanics lecture we have been discussing a simplified model of the Stern-Gerlach experiment. Let ##|+>## and ##|->## denote an electron that is "spin up" and "spin down" (with respect to ##\hat{z}##), respectively. Our professor then asserted that ##|+>## and ##|->## acted as a basis for a 2-D Hilbert space. It follows that a spin in ##\hat{x}## could then be constructed in the following way: $$|+_x > = \frac{1}{\sqrt{2}} ( |+> + |->)$$ however, this confuses me. How can we possible construct a ket pointing in ##\hat{x}## out of kets pointing in ##\hat{z}##??