Category: 2. A Simple Quantum System

Beam Amplitudes Spot intensity on screen Left Right as SG x is slowly turned off L R L R Final (SG x off) + + + − no spot − + no spot − − In the language of optics, we can say that the middle two beams, having 26 Introduction to Quantum Physics and…

Consider a sequence of Stern–Gerlach tests where an unpolarized beam passes through an SG z and subsequently through an SG x . Clearly there are four possible outcomes: a screen placed at the end will show up 4 spots as in Figure 2.8. If we place another SG z at the end, we expect eight…

An experiment such as that in Figure 2.6 represents a measurement out- come: the average value of the z-component of spin of the input beam is +1/2, obtained by the weighted probabilities of spin 1/2 at the up port and spin −1/2 at the down port, which in quantum notation is: hS z i |ii…

The magnetic moment, and therefore spin, has three spatial components, and we think of spin as a vector in space with x, y, and z components. To completely determine the spin of an electron, we would need to measure all three components. We could do this by setting up SG machines with magnetic inhomogeneities along…

A generic (unknown) state |ψi, before measurement in a particular basis, has the potential to be in either basis state. Suppose the probability am- plitudes for measuring the state to be |↑i is a complex number α and that for |↓i is β. We express this fact mathematically by writing |ψi as a linear superposition…

Let’s denote the (unknown but pure) input state of the electrons in the beam by |ii and the output state by |oi. The probability of obtaining this particular output is given by P(|ii → |oi) = no. of electrons in state |oi Total number of electrons in input beam . (2.2) We are going to…

The Stern–Gerlach setup of Figure 2.1 with the direction of inhomogeneity of the magnetic field defined as the z-axis is going to be the basis for defining 2 The standard unit for atomic magnetic moment is the Bohr Magneton, given by e~ 2m e c , numerically equal to about 5.8×10 −5 eV/T, where m…

Way back in 1922, when physicists were still studying the new and aston- ishing properties of the basic constituents of matter, an experiment designed 15 16 Introduction to Quantum Physics and Information Processing to measure the magnetic moment of atoms gave unexpected results. This was the classic Stern–Gerlach experiment [36], designed to measure the magnetic…