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finalexam - USEFUL CONSTANTS AND FORMULAS Physical...

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USEFUL CONSTANTS AND FORMULAS Physical constants and common integrals h = 6.63 10 34 J s = = 1.06 × 10 34 J s m e = 9.11 10 34 kg c = 3.0 8 m s × × × 10 Eh = ν = hc λ xp = 2 = h p λν = c Δ Δ e ax 2 dx = 1 π a x 2 1 2 2 n a x n ! xe dx = x e d x = 3 x d x = n + 1 0 2 a 0 2 a 0 4 a 2 0 a valid for n >− 1, a > 0 Fundamental equations ' = ( ) = H ˆ Ψ ( ) , t Time Dependent Schrödingers Equation i Ψ x , t x t = 2 2 + Vx () ψ x = E Time Independent Schrödinger's Equation x 2 m x 2 Canonical Commutation Relation [ ˆˆ , = xp ] i = = Heisenberg Uncertainty Principle σσ x p 2 2 2 Fermi's Golden Rule W fi = V fi δ ( E f E i = ω ) ( + E f E i + = ) = Vt = cos t fi 3 r * f V i r ˆ V ˆ ( ) V = d r ˆ Particle in a box ˆ = 2 2 0 0 < < xa H =− 2 mx 2 + V x V = everywhere else 222 n = n = 2 ( 0 x a ) = 2 E s i n n x 2 ma a a Separable systems ˆ ˆ ˆ ( , ) = H x + y ( ) Ψ m , xy ) = m x n y E , = E Hxy ( ) H y ( , ( ) ( ) + E x m m n
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Harmonic oscillator H ˆ =− 1 2 + 1 k x
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finalexam - USEFUL CONSTANTS AND FORMULAS Physical...

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