An equal superposition of two stationary states in an infinite well beats with period

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Quantum dynamics and its formulations · Symmetry, angular momentum and spin

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Spin one-half, the Pauli matrices and two-level systems

Problem

An equal superposition of two stationary states in an infinite well beats with period T=h/(E2−E1)T = h/(E_2-E_1), the energy gap between them. Ammonia's two stationary states are split by 2Δ=9.9×10−5 eV2\Delta = 9.9\times10^{-5}\ \mathrm{eV}. Write the full beat period of the double well in the same form, T=h/(2Δ)T = h/(2\Delta), and show it is exactly twice the crossing time t=1/2ν=2.1×10−11 st = 1/2\nu = 2.1\times10^{-11}\ \mathrm s found in this chapter's worked example.

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