130_notes.dvi

23.3 Examples 23.4 Derivations and Computations 23.4.1 The Relativistic Correction Moving from the non-relativistic formula for ...

Note that this was just a classical calculation which we will apply to quantum states later. It is correct for the EM forces, bu ...

Since this does not depend on eithermℓorj, totaljstates and the product states give the same answer. We will choose to use the t ...

23.4.6 The Anomalous Zeeman Effect We compute the energy change due to a weak magnetic field using first order Perturbation Theo ...

So adding this to the (easier) part above, we have E(1)n = eB 2 mc ( mj ̄h± mj ̄h 2 ℓ+ 1 ) = e ̄hB 2 mc mj ( 1 ± 1 2 ℓ+ 1 ) forj ...

an electron bound in a 3D harmonic oscillator? Give the energy shifts and and draw a diagram for the 0sand 1pstates. V=^12 mω^2 ...

24 Hyperfine Structure The interaction between the magnetic moment, due to the spin of the nucleus, and the larger magnetic mome ...

It is in the states of definitefandmfthat the hyperfine perturbation will be diagonal. In essence, we are doing degenerate state ...

See Example 24.3.2:The Hyperfine Splitting in a Weak B Field.* The result of this is example is quite simpleE=En 00 +A 2 ( f(f ...

0 0 500 E B full calc. strong field weak field We can make a more general calculation, in which the interaction of the nuclear m ...

∆Ef=1−∆Ef=0= 4 3 ( 1 137 ) 4 ( . 51 938 ) (. 51 × 106 )(5.56) = 5. 84 × 10 −^6 eV Recall that at room temperature,kBtis about 40 ...

24.3.3 Hydrogen in a Strong B Field We need to compute the matrix elements of the hyperfine perturbation using|msmi〉as a basis w ...

The top part is already diagonal so we only need to work in bottom right 2 by 2 matrix, solving the eigenvalue problem. ( A B B ...

are always exactly oposite each other in the center of mass and so the momentum vector we use is easily related to an individual ...

Let’s define our perturbationW as W≡ A ̄h^2 S~ 1 ·S~ 2 +w 1 S 1 z+w 2 S 2 z Here, we have three constants that are determined by ...

Then we compute the energy shift in first order perturbation theory for s states. ∆E= 〈 e mec S~·B~ 〉 =− Ze^2 gN 2 meMNc^2 ( S~· ...

We will sometimes group the constants such that ∆E≡ A ̄h^2 S~·~I. (The textbook has numerous mistakes in this section.) 24.5 Hom ...

25 The Helium Atom Hydrogen has been a great laboratory for Quantum Mechanics. After Hydrogen, Helium is the simplest atom we ca ...

Now let’s look at the (anti)symmetry of the statesof two identical electrons. For the ground state, the spatial state is symmetr ...

25.2 The Helium Ground State Calculating the first order correction to the ground state is simple inprinciple. ∆Egs=〈u 0 |V|u 0 ...