What is the expected value of a spin?

The expectation value. You can see that when a single spin ½ particle passes through the Stern-Gerlach apparatus oriented along the z‑axis, the only possible measurement outcomes for the spin component Sz are Sz = +ħ/2 (particle detected in the upper path), or Sz = –ħ/2 (particle detected in the lower path).

What is the expectation value of x?

This integral can be interpreted as the average value of x that we would expect to obtain from a large number of measurements. Alternatively it could be viewed as the average value of position for a large number of particles which are described by the same wavefunction.

How do you find the expectation value?

The expected value (EV) is an anticipated value for an investment at some point in the future. In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.

What are the appropriate eigenvector of Sz?

The only possible result of a measurement of an observable is one of the eigenvalues an of the corresponding operator A. These equations tells us that + 2 is the eigenvalue of Sz corresponding to the eigenvector + and “ 2 is the eigenvalue of Sz corresponding to the eigenvector “ .

How to calculate the expectation value of S ^ X?

Closed 5 years ago. Consider the state-space with a base formed by the eigenstates of the operator S ^ z. For the state | ϕ ⟩ = 1 2 | + ⟩ z − 1 2 | − ⟩ z, what is the value of ⟨ S ^ x ⟩?

How does the spin-statistics theorem relate to quantum states?

The spin–statistics theorem states (1) that particles with half-integer spin (fermions) obey Fermi–Dirac statistics and the Pauli Exclusion Principle, and (2) that particles with integer spin (bosons) obey Bose–Einstein statistics, occupy “symmetric states”, and thus can share quantum states.

Why do you need a matrix for spin operators?

In this case, you have to perform the calculation. The matrix formulation of the spin operators makes the calculations faster and easier than they would be when you explicit writing out everything in terms of the zbasis states. We could also quickly figure out what the amplitude for measuring positive xspin is with this formalism.

How to find the operator for spin in an arbitrary direction?

The operator S u has eigenvalues of ±ħ2, just like the usual spin matrices. This method of finding the operator for spin in an arbitrary direction generalizes to higher spin states, one takes the dot product of the direction with a vector of the three operators for the three x-, y-, z-axis directions.