7.6b Hyperfine labs

Source: Lab ideas from Computational Physics (Landau, Páez, Bordeianu), §7.6. Rewritten as original drills. Continues 7.6 Spin states and hyperfine.

Explorer

Pure Python lists. Build hyperfine $V$ for $W=1$ from the theory walk (spectrum $-3,1,1,1$; $\Delta E/W=4$).

Formula refresh

Warm up: pick the matching equation among lookalikes (same walk as the theory lesson).

Labs

Activity: Build $V$ for $W=1$

Return $V$ as a $4\times 4$ list of lists. Print all 16 entries row-major, space-separated integers.

No input.

Write-ups

0/4 solved

7.6b.W1

Using “triplet”, “singlet”, and “W”, explain:

For this V matrix, which multiplet sits at +W and which at −3W?

Minimum 3 words. Your answer must include: “triplet”, “singlet”, “W”.

0 words/ 3 min

Meet the writing requirements, then you can open the model answer.

Explorers

# hyperfine_ref.py — V(W) spectrum (original sketch)
def build_V(W=1.0):
    return [
        [W, 0, 0, 0],
        [0, -W, 2 * W, 0],
        [0, 2 * W, -W, 0],
        [0, 0, 0, W],
    ]

def spectrum(W=1.0):
    return sorted([W, W, W, -3 * W])  # ΔE/W = 4

Next: 7.7 Speeding up matrix computing.