8Experiment 8

Quantum Tunneling and Transmission Resonances

Measure exact barrier transmission T (with T+R=1 conservation check), observe exponential width dependence, and locate above-barrier resonances.

A. Barrier parameters & transmission

Particle:

Energy E (eV)0.50 eV

Barrier V₀ (eV)1.00 eV

Width a (nm)0.50 nm

T (exact)1.0138e-1

R (exact)8.9862e-1

T + R1.0000000000

RegimeE < V₀ — tunneling

κ⁻¹ = ħ/√(2m(V₀−E))0.276 nm

κa (controls exp. decay)1.811

Scan variable:

T vs. chosen variable. Red dot = current setting. Dashed gold = V₀ (for E scan).

B. Scattering wavefunction

t = 0.000 fs

Re ψ(x,t) |ψ(x)|² (static) V(x)

|ψ(x)|² is exactly static for a stationary scattering state — only the phase evolves. Standing-wave fringes on the left (incident + reflected), evanescent/oscillatory profile inside the barrier, travelling wave on the right.

Observations

Record your measured data in the tables below. Refer to the lab manual for the full procedure.

Table 8.1 — Tunneling below the barrier ( $E < V_{0}$ )

a (nm)	V₀ (eV)	T	R	T+R

Table 8.2 — Resonance search ( $E > V_{0}$ )

Resonance search	Value found	T

Rows: Width at T≈1; Width at T minimum; Energy at T maximum