An electron with energy eV meets a potential step of height eV

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Free particles, wave packets and tunnelling

Problem

An electron with energy E=0.8E = 0.8 eV meets a potential step of height V0=1.5V_0 = 1.5 eV, so E<V0E < V_0. Find the decay constant κ\kappa of the wave function inside the step, and find what fraction of the density at the step's edge remains at a depth of 0.150.15 nm inside it. Use ℏ2/2me=0.0381\hbar^2/2m_e = 0.0381 eV nm2^2.

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