Quantum Mechanics Concepts
104 flashcards by MentisLibrary
Planck and de Broglie relations, the Schrödinger equation, operators and commutators, the hydrogen atom and quantum numbers, the particle in a box and harmonic oscillator, tunneling, measurement and entanglement, spin and statistics, and quantum information. For undergraduate physics students.
- What is the Planck-Einstein relation?
- E = hf
- What is the value of Planck's constant?
- h = 6.626 × 10⁻³⁴ J·s
- What is the de Broglie wavelength?
- λ = h/p
- What is the Heisenberg Uncertainty Principle (position-momentum)?
- Δx Δp ≥ ℏ/2
- What is the Heisenberg Uncertainty Principle (energy-time)?
- ΔE Δt ≥ ℏ/2
- What is the time-independent Schrödinger equation?
- Ĥψ = Eψ
- What is the time-dependent Schrödinger equation?
- iℏ ∂ψ/∂t = Ĥψ
- What is the Hamiltonian operator in 1D?
- Ĥ = -ℏ²/(2m) d²/dx² + V(x)
- What is the momentum operator?
- p̂ = -iℏ d/dx
- What is the position operator?
- x̂ = x
- What is the energy operator?
- Ê = iℏ ∂/∂t
- What is the commutator of position and momentum?
- [x̂ p̂] = iℏ
- What is the normalization condition for wavefunction?
- ∫|ψ|² dx = 1
- What is the expectation value formula?
- ⟨A⟩ = ∫ψ* Â ψ dx
- What is the probability density?
- ρ(x) = |ψ(x)|²
- What is the wave-particle duality?
- Particles exhibit both wave and particle properties
- What is the photoelectric effect equation?
- KEmax = hf - φ
- What is the Compton wavelength?
- λc = h/(mc)
- What is the Compton scattering formula?
- λ' - λ = (h/mc)(1 - cos θ)
- What is the Rydberg formula for hydrogen?
- 1/λ = R(1/n₁² - 1/n₂²)
- What is the Bohr radius?
- a₀ = 4πε₀ℏ²/(me²)
- What is the energy of hydrogen atom in Bohr model?
- En = -13.6 eV/n²
- What is the angular momentum in Bohr model?
- L = nℏ
- What are the quantum numbers for hydrogen atom?
- n (principal); l (orbital angular momentum); ml (magnetic); ms (spin)
- What is the orbital angular momentum magnitude?
- L = √(l(l+1)) ℏ
- What is the z-component of angular momentum?
- Lz = ml ℏ
- What is the spin angular momentum?
- S = √(s(s+1)) ℏ
- What is the z-component of spin?
- Sz = ms ℏ
- What is the Pauli Exclusion Principle?
- No two fermions can occupy the same quantum state
- What is the fine structure constant?
- α = e²/(4πε₀ℏc) ≈ 1/137