new lecture notes

lecture_notes/4-4/overview

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+                    Review of Braket notation
+━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
+Moving toward the interaction of two spins
+
+(pic) Set up one spin Braket notation
+
+(pic) some spin geometry, showing how certain currents attract eachother
+
+
+                            Two Spins
+━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
+Chapter 5 - Two Spins
+
+(pic) 𝐒₁⋅𝐒₂  OR 2A/ħ²𝐒₁⋅𝐒₂ in book
+
+hydrogen spin-orbit hamiltonian Ĥ = -γ 𝐒⋅𝐋
+
+4 possible states
+
+    ❙S₁𝓏=+½ S₂𝓏=+½❭ = ❙½❭⨂❙½❭
+    ❙S₁𝓏=+½ S₂𝓏=-½❭
+    ❙S₁𝓏=-½ S₂𝓏=+½❭
+    ❙S₁𝓏=-½ S₂𝓏=-½❭
+
+        (pic) expanded ❙½❭⨂❙½❭
+
+
+(pic x2) finding representations for all of the operators in the two-spin system
+
+(pic) Worked out some operations on various possible states, using direct product spaces
+
+(pic x2) Diagonalized 𝐒₁⋅𝐒₂
+
+    !!! missing a factor of 2 somewhere in these pictures
+
+    
+    

lecture_notes/4-5/overview

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+Started with vector potential
+
+    (pic) Demonstrated why 𝐉ᵦ = ∇×𝐌
+
+(pic) Find magnetic field of a uniformly magnetized sphere
+
+    this development ended up converging with the sphere of constant surface charge
+
+
+(pic) Started with a reminder of displacement definition and origin.
+
+    (pic) This leads to an analogy with 𝐉ₜₒₜ = 𝐉𝒻 + 𝐉ᵦ
+
+    leads to very useful ∮𝐇⋅d𝐥 = 𝐈𝒻(s)
+
+Bit of an aside about how 𝐇 is easier to measure/control compared to 𝐁.
+
+(pic) An example of finding 𝐁 outside a thick rod.
+
+    actually didn't develop this, but just warned about that M has a
+    divergence at the edges, so 𝐇 is not so easy to find.
+
+Introduced linear materials
+
+    𝐌 = χₘ 𝐇
+
+    χₘ > 0 (paramagnetic)
+
+    χₘ < 0 (diamagnetic)
+
+    Example: an infinite solenoid carrying a surface current 𝐊 = K ϕ̂ filled
+    with material of susceptibility χₘ. Find 𝐁.
+
+        (pic) found 𝐇, then 𝐁, then bound and free 𝐊