4Experiment 4
The Infinite Square Well: Energy Quantization
Verify exact energy levels (Eₙ ∝ n²), count wavefunction nodes, compare electron vs. proton energies, and observe time-evolved superpositions.
A. Energy levels and wavefunctions
1.00 nm
1
| n | Eₙ (eV) | nodes | Eₙ/E₁ |
|---|---|---|---|
| 1 | 0.37607 | 0 | 1.0000 |
| 2 | 1.50426 | 1 | 4.0000 |
| 3 | 3.38459 | 2 | 9.0000 |
| 4 | 6.01706 | 3 | 16.0000 |
| 5 | 9.40165 | 4 | 25.0000 |
| 6 | 13.53838 | 5 | 36.0000 |
Eₙ = n²π²ℏ²/(2mL²). Click a level in the diagram to select it.
ψₙ(x) |ψₙ(x)|²
B. Superposition and time development
t = 0.00 fs
Single eigenstate: |ψ(x,t)|² is exactly frozen (stationary state). Add a second state to see genuine oscillation at the beat frequency (E₂−E₁)/ℏ.
Observations
Record your measured data in the tables below. Refer to the lab manual for the full procedure.
Table 4.1 — Energy levels and nodes (electron, nm)
| n | Eₙ (eV) | Nodes | Eₙ/E₁ |
|---|---|---|---|
Table 4.2 — Ground-state energy dependence
| Setting | E₁ (eV) |
|---|---|
Rows: Electron L=1 nm; Electron L=0.5 nm; Proton L=1 nm