Lecture_3 - 5. The Quantum Mechanical Model of the Atom W ....

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1 5. The Quantum Mechanical Model of the Atom Wave mechanics or Quantum mechanics By analogy with a guitar string, fastened at both ends: DeBroglie L dinger o Schr E Heisenberg W . . . & & Particles take on wave properties: view the electron as a standing wave! • If we assume a circular trajectory , we should have: Circumference a whole number of wavelengths Cancellation by destructive interference
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2 2 2 rn h mr n n h But m πλ π λ = ⇒= = = (De Broglie) h v v Bohr assumption! ± Schr ö dinger (1925): Wave equation to calculate the total energy of the atom. Idea : particle is distributed in space just like the amplitude of a wave. A high intensity is equivalent to a high probability of finding the particle! Schrödinger wave equation (SWE) Ψ E Ψ H = ˆ E H ˆ Ψ wave function Hamiltonian operator Total energy z) y, (x, Ψ V T ˆ ˆ + E P E K . . + of the moving electron of attraction between e and the nucleus ²
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Lecture_3 - 5. The Quantum Mechanical Model of the Atom W ....

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