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Quantum mechanics unit 1

Quantum mechanics unit 1. Foundations of QM Photoelectric effect , Compton effect, Matter waves The uncertainty principle The Schr ö dinger eqn. in 1D Square well potentials and 1D tunnelling The harmonic oscillator. Dr Mervyn Roy (S6)

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Quantum mechanics unit 1

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  1. Quantum mechanics unit 1 • Foundations of QM • Photoelectric effect, Compton effect, Matter waves • The uncertainty principle • The Schrödinger eqn. in 1D • Square well potentials and 1D tunnelling • The harmonic oscillator Dr Mervyn Roy (S6) www2.le.ac.uk/departments/physics/people/academic-staff/mr6 www.le.ac.uk/physics -> people -> Mervyn Roy

  2. Resources Quantum Mechanics, Alastair I. M. Rae • Chapters 1 and 2 for unit 1 Physics for scientists and engineers, P. A. Tipler Concepts of modern physics, A. Beiser 114, 214 Course notes Library - Schiff, Mandl etc. www Staff

  3. Classical to Quantum Start of the 19th century: The importance of QM #1: ~25 years, 9 Nobel prizes Classical - continuous, deterministic Quantum - discrete, probabilistic

  4. The need for a quantum theory 1 Classical theory works well but… • UV Catastrophe • Photoelectric effect • Compton effect …waves as particles

  5. Photoelectric effect Observed by Hertz 1887. Explained by Einstein 1901, Nobel prize 1918

  6. Compton effect A. H. Compton, Phys. Rev. 21 483 (1923). Nobel prize 1927

  7. The need for a quantum theory 2 Classical theory works well but… • Discrete atomic spectra • de Broglie waves • Electron diffraction …particles as waves

  8. Discrete spectral lines • Atoms must have discrete energy levels • Bohr, 1913. Nobel prize 1922 • The importance of QM #2: Used everywhere in physics – Nano, Space, Planetary, Astrophysics

  9. Matter waves • de Broglie hypothesis • 1924 - speculated that matter has wave-like character • Nobel prize 1929 • 1927 Experimental evidence • Electron diffraction • Observed by Davisson and Germer and, independently, by Thomson • Nobel prize 1937 (for Davisson and Thomson)

  10. Example • Calculate: • wavelength of free electron, E = 50 eV • wavelength of golf ball, v= 30 ms-1, m=0.046 kg l = 0.17 nm l = 4.8 x 10-34 m

  11. lnm atomic spacing X-rays electrons neutrons Quantum interference of large organic molecules, S. Gerlichet al, Nature Communications 2 263, 2011 C168H94F152O8N4S4(430 atoms)

  12. Probability waves (Born’s postulate 1926, Nobel prize 1954) Electron interference - double slit experiment with electrons

  13. Wave particle duality • Light and matter sometimes behave like waves and sometimes like particles – depends on experiment • Wave and particle pictures are complementary It is often stated that of all the theories proposed in this century, the silliest is quantum theory. In fact, some say that the only thing that quantum theory has going for it is that it is unquestionably correct. - MichioKaku, Hyperspace (1995) The importance of QM #3: Technology– solid state transistors, e-beam lithography, atomic clocks (GPS), SQUIDs & MRI, Quantum communication/cryptography, Lasers etc. etc.

  14. Wave particle duality • ...the "paradox" is only a conflict between reality and your feeling of what reality "ought to be." Richard Feynman, The Feynman Lectures on Physics, (1965) What am I? Rae, chapter 13. In Search of Schrödinger’s Cat, John Gribbin

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