Quantum Mechanics

Use this for “An electron is in state n = 2 of a 0.5 nm box. Find ⟨x⟩, Δx and Δp, and check the uncertainty principle.”

Use this for “A particle in a box is in the state 3ψ₁ + 4ψ₂, with E₁ = 0.2 eV. What energies can a measurement give, with what chances, and what is ⟨E⟩?”

Use this for “Can the position x and the momentum pᵧ of an electron both be known exactly at once?”

Use this for “A molecule vibrates at ω = 5.6 × 10¹⁴ rad/s. Find its zero-point energy, the energy of level n = 2 and the wavelength of the photon of one step down.”

Use this for “An electron meets a barrier 0.3 eV above its energy and 1.2 nm wide. Estimate the chance that it tunnels through.”

Use this for “Electrons of 9 eV meet a potential step 5 eV high. What fraction is reflected, and what fraction goes on?”

Use this for “An electron leaves a Stern–Gerlach magnet spin up along z and enters a second magnet tilted 120° from z. Find the chances of up and down and the average reading.”

Use this for “An atom in a p state (ℓ = 1) sits in a 0.5 T field. How far apart are its levels, how many are there, and at what frequency does a free electron’s spin flip?”

Use this for “A d electron has ℓ = 2 and spin s = ½. Which total j can it have, how many states does each hold, and how many states are there in all?”

Use this for “Levels at 0.2 eV and 0.7 eV are mixed by a coupling of 0.05 eV. Find the exact levels and compare the lower one with second order.” Two equal levels (degenerate) split to E₁ ± V.

Use this for “What is the chance of finding hydrogen’s ground-state electron within one Bohr radius of the nucleus?”

Use this for “Find the ground-state energy of muonic hydrogen (a muon, 206.8 mₑ, round a proton).”