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Physics 451

Delve into the quantum mechanics of the hydrogen atom, studying the probability density of electrons, angular equations, radial equations, Coulomb's law, and asymptotic behaviors. Dive into the quantization of energy, degeneracy of energy levels, and energy transitions. Uncover key concepts like quantum numbers, Bohr radius, stationary states, and spectroscopy. Challenge yourself with quizzes on quantum numbers and energy bands.

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Physics 451

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  1. Physics 451 Quantum mechanics I Fall 2012 Nov 5, 2012 Karine Chesnel

  2. Quantum mechanics Announcements • Homework this week: • HW #17 Tuesday Nov 6 by 7pm • HW #18 Thursday Nov 8 by 7pm

  3. Quantum mechanics The hydrogen atom What is the density of probability of the electron?

  4. The angular equation (same) Angular function (same) l Azimutal quantum number m Magnetic quantum number Phys 451 The hydrogen atom

  5. The radial equation Coulomb’s law: Phys 451 The hydrogen atom

  6. The radial equation Phys 451 The hydrogen atom Asymptotic behaviors

  7. Peeling off the asymptotic behaviors Power expansion Recursion formula: Phys 451 The hydrogen atom

  8. Principal quantum number Phys 451 The hydrogen atom The series must terminate

  9. Quantum mechanics Quiz 23a For a given quantum number n, how many values of l can exist? A. one B. two C. n D. n -1 E. An infinity

  10. Quantization of the energy Bohr 1913 Ground state: “binding energy” Quantum mechanics The hydrogen atom Principal quantum number

  11. Bohr radius Quantum mechanics The hydrogen atom

  12. Stationary states l: azimuthal quantum number m: magnetic quantum number Degeneracy of nth energy level: Quantum mechanics The hydrogen atom Energies levels n: principal quantum number

  13. Quantum mechanics Quiz 23b What is the degeneracy of the 5th energy band of the hydrogen atom? A. 5 B. 9 C. 11 D. 25 E. 50

  14. E 0 E4 E3 Energy transition Paschen E2 Balmer E1 Rydberg constant Lyman Quantum mechanics The hydrogen atom Spectroscopy Energies levels

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