s 27.1 The Heisenberg uncertainty principles The Heisenberg uncertainty principle states that there exists a fundamental limit to the extent to which we can simultaneously determine the position and corresponding momentum component of a wave-particle any given direction 2. The energy-time uncertainty principle Recall mathematical form of a monochromatic wave Y(x, t)=Acos(kx-at) 2丌 Acos(x-2riv) 8 27.1 The Heisenberg uncertainty principles Substitution for a and v h E=hv P 2丌 Y(x, +)=AcoS(Px 2兀E The role of e and t in the equation are mathem- atically identical to the role ofx and p ∠EMt2h 3.The implications of the uncertainty principles o the uncertainty principle indicate that it is not exact describing the microscopic particle by classical theory.3 The Heisenberg uncertainty principle states that there exists a fundamental limit to the extent to which we can simultaneously determine the position and corresponding momentum component of a wave-particle in any given direction. 2. The energy-time uncertainty principle 2 ) 2 cos( ( , ) cos( ) A x t x t A kx t πν λ π Ψ ω = − = − Recall mathematical form of a monochromatic wave §27.1 The Heisenberg uncertainty principles λ E hν p h x = , = Substitution for λ and ν ) 2 2 ( , ) cos( Et h p x h x t A x π π Ψ = − The role of E and t in the equation are mathem￾atically identical to the role of x and px. ∆E∆t ≥ h 3.The implications of the uncertainty principles 1 the uncertainty principle indicate that it is not exact describing the microscopic particle by classical theory. §27.1 The Heisenberg uncertainty principles