Yes, your solution is correct. The answer in the problem statement is incorrect. They should have left out the matrix Sy in the calculation of the probability. Note that the probability must be a dimensionless number, but they are getting something that has the dimensions h2.bbnl1990 said:Isn't the probability of measuring h-bar/2 the same as the probability of finding the particle in the state ψ+?
Yes, your solution is correct. The answer in the problem statement is incorrect. They should have left out the matrix Sy in the calculation of the probability. Note that the probability must be a dimensionless number, but they are getting something that has the dimensions h2.
In quantum mechanics, h-bar/2 refers to the reduced Planck's constant, which is a fundamental constant used to describe the behavior of particles at the quantum level.
In quantum mechanics, Sy refers to the spin of a particle along the y-axis. Measuring Sy allows us to determine the spin state of a particle and make predictions about its behavior.
The probability of the result h-bar/2 if Sy is measured represents the likelihood of obtaining a spin measurement of h-bar/2 along the y-axis. This probability is calculated using the principles of quantum mechanics and can vary depending on the specific system being studied.
The probability of h-bar/2 if Sy is measured is calculated using the Schrödinger equation, which describes the evolution of quantum systems. This equation takes into account the initial state of the system, the measurement being made, and the properties of the system itself to determine the probability of obtaining a specific measurement result.
The probability of h-bar/2 if Sy is measured can also be affected by external disturbances or interactions with other particles. Additionally, the uncertainty principle in quantum mechanics states that it is impossible to know the exact values of certain properties, such as position and momentum, simultaneously. This uncertainty can also impact the probability of obtaining a specific measurement result.