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your computer, and then open the ﬁle again. If the red x still appears, you may have to delete the image and then insert it again. 27 Example: Zeeman Splikng u༇ How do the l=1 states split in a 1 T B- ﬁeld? o ΔE=µBBml o ΔE=5.788×10−5 eV (1)ml
u༇ A small shiG in energy. u༇ Three m states have diﬀerent energies. 28 Limited visible lines due to selec2on rules u༇ while all lines are possible energy diﬀerences, only the colored ones are strongly visible. u༇ E1 limited to Δl=±1 and Δm=0,±1 and Δs=0 due to photon emission rules 29 Anomalous Zeeman Splikng Observed u༇ OGen splikng into an even number of lines was observed u༇ Some2mes, the lines were not equally spaced u༇ The correct explana2on of the anomalous Zeeman eﬀect involves electrons spin and is rather complicated. 30 Electron Spin u༇ The anomalous Zeeman eﬀect measurements indicated something was wrong with the normal Zeeman theory. u༇ An experiment by Stern and Gerlach measuring the splikng of a beam of silver atoms in a high B ﬁeld gradient showed a split into two beams. o not expected for any l
o needed spin ½ u༇ Uhlenbeck and Goudsmit propose electron spin in 1925. 31 Spin u༇ Internal angular momentum u༇ Electron has spin s=½ (ms=± ½ ) o two state system o an2symmetric under interchange o implies no two in same state o only created as par2cle an2par2cle pair o maOer par2cle u༇ Photon has spin 1 o symmetric (under interchange) o implies as many par2cles in same state (LASER) o can be created singly o Energy par2cle 32 Spin Magne2c Moment u༇ A spin ½ par2cle has a z component of spin which is either +½ or –½ when measured along any axis (quan2zed). u༇ Correspondingly, the magne2c moment along any axis is quan2zed to be either plus or minus one Bohr magneton. u༇ Orbital angular momentum moment is same size for l=1. u༇ If a B ﬁeld is applied, the states can be split. Stern- Gerlach (1922) Pass collimated beam through B ﬁeld gradient. u༇ Force on par2cles propor2onal to z component of magne2c moment. u༇ Shows quan2zed nature of magne2c moment. u༇ In 1922 S- G observed Ag beam split into 2. u༇ o hard to understand for just orbital angular momentum. u༇ S- G experiment helps illustrate many concepts of angular momentum in QM. 34 The Two State System u༇ With just two states, we only need 2 complex amplitudes....
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