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EE201/MSE207 Applied Quantum Mechanics Lecture 1: Introduction Quantum mechanics (QM) is one of two theories of 20 th century physics, which considerably changes our understand of nature. - Relativity changed our understanding of space and time.

  1. EE201/MSE207 Applied Quantum Mechanics Lecture 1: Introduction Quantum mechanics (QM) is one of two theories of 20 th century physics, which considerably changes our understand of nature. - Relativity changed our understanding of space and time. - QM changed the logic of thinking about microscopic objects. Main philosophical ideas: wave-particle duality and indeterminism 𝐹 = β„πœ• (Planck-Einstein) for particles ℏ = 1.05 Γ— 10 βˆ’34 J οƒ— s 2πœŒβ„ πœ‡ = π‘ž (de Broglie) for particles Estimates: 2πœŒβ„ 1.504 eV 1.226 nm Electron: πœ‡ = 2𝑛 𝑓 𝐹 = 1 nm = 𝐹 𝐹[eV] 2πœŒπ‘‘ 2πœŒβ„π‘‘ 1.240 𝜈m Photon: πœ‡ = πœ• = = 𝐹 𝐹[eV]

  2. Prehistory of Quantum Mechanics 1) 1900 Max Planck: suggested discrete absorption and emission of light to explain experimental formula for black-body radiation (Nobel Prize 1918) 𝐹 = β„Žπœ‰ = β„πœ• β„Ž = 6.63 Γ— 10 βˆ’34 J οƒ— s ℏ = 1.05 Γ— 10 βˆ’34 J οƒ— s 2) 1905 Albert Einstein: theory of photoelectric effect (Nobel Prize 1921) 𝑛𝑀 2 β„Žπœ‰ = Ξ¦ + Ξ¦ is work function (ionization energy) 2 3) 1913 Niels Bohr: model of atom (Nobel Prize 1922) 𝑛𝑀𝑠 = π‘œβ„ Discrete atomic spectra and Rutherford’s experiments (1910 -1911, N.P. 1908) 4) 1923 Arthur Compton: scattering of X-rays on electrons (Nobel Prize 1927) 5) 1923 Louis de Broglie: matter waves (theory only, in 1927 confirmed for πœ‡ = 2πœŒβ„ electrons, Nobel Prize 1929) π‘ž β€œBirth” of Quantum mechanics: 1927 (5 th Solvay conference, Brussels)

  3. Classical mechanics vs. Quantum Mechanics (one particle in one dimension) Classical mechanics: 𝑒 2 𝑦 𝑒𝑦 Position 𝑦(𝑒) , velocity 𝑀 𝑒 = 𝑒𝑒 , acceleration 𝑏 𝑒 = 𝑒𝑒 2 π‘’π‘Š(𝑦) 𝐺 = βˆ’ for a conservative system, π‘Š(𝑦) is potential energy 𝑒𝑦 𝐺 Main evolution equation: 𝑏 = 𝑛 𝑒 2 𝑦 𝑒𝑒 2 = βˆ’ 1 π‘’π‘Š initial conditions: οƒž 𝑦(𝑒) 𝑦 0 , 𝑦(0) 𝑛 𝑒𝑦 Quantum mechanics: Main evolution equation: SchrΓΆdinger equation πœ–π‘’ = βˆ’ ℏ 2 πœ– 2 Ξ¨ 𝑗ℏ πœ–Ξ¨ Ξ¨(𝑦, 𝑒) is a complex function, characterizing πœ–π‘¦ 2 + π‘ŠΞ¨ 2𝑛 the particle state (wave function) 2 𝑒𝑦 is the probability to find the particle between 𝑦 and 𝑦 + 𝑒𝑦 Ξ¨ 𝑦, 𝑒 at time 𝑒 (if observed!) Indeterminacy: particle does not have position (still debates about philosophy)

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