Question

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2. A quantum object whose state is given by lys)- a Stern-Gerlach device with the magnetic field oriented in the y-direction. What is the probability that this object will emerge from the + side of this device? +),-212 İs sent through 3. McIntyre, Chapter 2, Problem 23 4. Suppose that operators A and B are both Hermitian, i.e., At-A and B. B Answer the following and show your work: (a) Is A Hermitian? (b) Is AB Hermitian? (c) Is AB+BA Hermitian? (d) Is it possible for A to have complex eigenvalues, or must they be real?

Answer 1

This answer gives a solution for the Probability of +ve side Orientation of Quantum Object

Given quantum object state: psi = 1/2 + >_z - squareroot 3/2 - >_z with magnetic field orientation Y - direction psi > = 1/2 + >_z - squareroot 3/2 - >_z convertion to analog form psi > = cos phi/2 + > + sin phi/2 - > Then, The probability of orientation object will Emerge from the + side is, P(t) = < z, + psi > ^2 where < z, + > + > + - > /squareroot 2 because Now sin phi/2 = 1/2 cos phi/2 = -squareroot 3/2 Therefore phi/2 = 5/3 pi phi = 10 pi/3 P(t) = 1/2 cos phi/2 + sin phi/2^2 P(t) = 1 + sin phi/2 = 1 - squareroot 3/2/2 P(t) = 2 - squareroot 3/4 P(t) = 0.066