Quantum Theory - Quantum Mechanics - Lecture notes | PHYS 410, Study notes of Physics

Download Quantum Theory - Quantum Mechanics - Lecture notes | PHYS 410 and more Study notes Physics in PDF only on Docsity! Physics 410 - Quantum Mechanics Administrivia: info for me and you • syllabus • homework • exams • timeline • questionaire Lecture 1 Outline • History of Quantum theory (summary of modern physics) old quantum theory (in a page) • 1900 Planck quanta theory → E = nε0 = nhν = nhc/λ. • 1905 Einstein’s photoelectric effect theory → 1 2 mv2 max = hν − W . • 1911 Rutherford, Geiger, Marsden → nucleus ≈ 10−14 m, atom ≈ 10−10 m. • 1913 Bohr’s stationary (circular) states of the hydrogen atom → hν = Eb − Ea, and L = mvr = n~. • 1914 Franck and Hertz → energy quantisation of atoms . • 1921-1922 Stern and Gerlach → Lz = m~ and ℓ = 1 2 . • 1923-1924 de Broglie matter waves → v = E/h, λ = h/p. 1-D Classical Mechanics • Force: F (x, t) = m a(x, t).





x(t) F(x,t) m V(x,t) Newton’s Law: m d2x dt2 = − ∂V ∂x 1-D Schrödinger Equation • Given a wavefunction Ψ(x, t) (ie. a complex number) • Born’s statistical interpretation: prob. of measuring the particle/s between points a and b = ∫ b a |Ψ(x, t)|2dx V(x,t) a b 2(x,t)Ψ i~ ∂Ψ(x, t) ∂t = − ~ 2 2m ∂2Ψ(x, t) ∂x2 + V (x, t)Ψ(x, t) Statistical interpretation / measurement • Suppose that we do measure the particle/s near point c: 2(x,t)Ψ 2(x,t)Ψ c (i) before measurement (ii) measurement • this is known as wavefunction collapse, ie. • repeating the measurement also finds particle/s near c. • Statistical interpretation implies a indeterminancy...