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Ex2-5210

# Ex2-5210 - EXAM INFORMATION Harmonic Oscillator Hamiltonian...

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Unformatted text preview: EXAM INFORMATION Harmonic Oscillator Hamiltonian: Energy Levels: Anharmonic Oscillator Energies: Rigid Rotor Hamiltonian: Quantum Numbers: J = 0, 1, 2, 3, ... M=0, ±1, ±2, ..., ±J Energy Levels: Moment of Inertia: Linear Polyatomic: Diatomic: Boltzmann Distribution: First Order Perturbation Theory: INTEGRALS Constants and Conversions: h = 6.63x10-34 J·s ħ = h/2 π = 1.05x10-34 J·s k = 1.38x10-23 J/K c = 3.00x10 8 m/s = 3.00x10 10 cm/s N A = 6.02x10 23 mol-1 1 Å = 10-10 m 1 amu = 1.66x10-27 kg 1 J = 1 kg·m 2 /s 2 1 N = 1 kg·m/s 2 2 2 2 2 2 1 2 kx dx d H +- = μ μ πν ϖ ϖ k n n E n = = = + = 2 , 2 , 1 , 2 1 & ∑ = 2 i i r m I 2 1 2 1 2 m m m m r I + = = μ μ ∫ = ∆ τ ψ ψ d H E ) ( ) 1 ( ) ( * kT E i i i e g N /- ∝ ∫ ∫ ∫ ∫ ∞- ∞- ∞- ∞- = = = = 3 6 2 4 2 16 15 8 3 4 1 2 1 2 2 2 2 β π β β π β β π β β π β β β β dx e x dx e x dx e x dx e x x x x ∂ ∂ + ∂ ∂ ∂...
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Ex2-5210 - EXAM INFORMATION Harmonic Oscillator Hamiltonian...

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