==Imagine that we have a box that emits electrons in a definite but unknown spin state y). Ifwe send electrons from this box through an SGz device, we find that 20% are determined tohave Sz+ħ and 80% to have S₂ -ħ. If we send electrons from this box through anSGx device, we find that 90% are determined to have Sx +ħ and 10% to have SxDetermine the state vector for electrons emerging from the box. You may assume that thevector components are real.-1/ħ.=-

This can be solved using concepts of probability in quantum mechanics

Imagine that we have a box that emits electrons in a definite but unknown spin state |y). If we send electrons from this box through an SGz device, we find that 20% are determined to have S₂ = +¹ħ and 80% to have S₂ = − ½ħ. If we send electrons from this box through an SGx device, we find that 90% are determined to have Sx +ħ and 10% to have Sx=-1¹ħ. Determine the state vector for electrons emerging from the box. You may assume that the vector components are real. =

Imagine that we have a box that emits electrons in a definite but unknown spin state |y). If we send electrons from this box through an SGz device, we find that 20% are determined to have S₂ = +¹ħ and 80% to have S₂ = − ½ħ. If we send electrons from this box through an SGx device, we find that 90% are determined to have Sx +ħ and 10% to have Sx=-1¹ħ. Determine the state vector for electrons emerging from the box. You may assume that the vector components are real. =