Lecture physics a2 introduction to quantum physics matter waves and the schrödinger equation huynh quang linh

“‘Quantum mechanics’ is the description of the behavior of matter and light in all its details and, in particular, of the happenings on an atomic scale Things on a very small scale behave like nothing[.]

“‘Quantum mechanics’ is the description of the behavior of matter and light in all its details and, in particular, of the happenings on an atomic scale Things on a very small scale behave like nothing that you have any direct experience about They not behave like waves, they not behave like particles, they not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.” Richard P Feynman Lecture 6: Introduction to Quantum Physics: Matter Waves and the Schrödinger Equation Content  Electron Diffraction  Matter-wave Interference   particles as waves  Composite particles  Electron microscopy  Heisenberg Uncertainty Principle Schrödinger Equation (SEQ)   Time-independent SEQ gives static solutions for wavefunctions Physical interpretation of the wavefunction Matter Waves  DeBroglie (1924) proposed that, like photons, particles have a wavelength: l = h/p  electron gun detector q Inversely proportional to momentum In 1927-8, it was shown (DavissonGermer) that, like x-rays, ELECTRONS can also diffract off crystals ! Ni Crystal Interference peak ! • We will see later that the discrete atomic emission lines also arise from the wavelike properties of the electrons in the field of the nucleus: Atomic hydrogen I(q) Electrons can act like waves!! 60 q What does this mean? In discussion section: q o “Double-slit” Experiment for Electrons     Electrons are accelerated to 50 keV  l = 0.0055 nm Central wire is positively charged  bends electron paths so they overlap A position-sensitive detector records where they appear lp Exrcise 1: Matter wavelengths  What size wavelengths are we talking about? Consider a photon with energy eV, and therefore momentum p = eV/c Its wavelength is: h 4.14 1015 eV  s l   c  1.4 1015 s  108 m / s  414 nm p eV    What is the wavelength of an electron with the same momentum? a) le = lp b) le < lp c) le > lp le = h/pe   Same relation for particles and photons Note that the kinetic energy of the electron is different from the energy of the photon with the same momentum (and wavelength): KE   34  p h 6.625  10 J s  24    41  10 J  31  2m 2ml 2( 9.11 10 kg )( 414  10 m ) 2  1.602  1019 J / eV  8.8  106 eV Compared to the energy of the photon (given above): E  pc  3eV Wavelength of an Electron  The DeBroglie wavelength of an electron is inversely related to the electron momentum: l = h/p  Frequently we need to know the relation between the electron’s wavelength l and its kinetic energy E p and E are related through the classical formula: p2 E 2m h2 E 2ml p = h/l For m = me: (electrons) Don’t confuse with E 1.505 eV  nm2 E photon  l2 1240 eV  nm l m e  9.1110-31kg always true! h  4.14 10-15eV  s E in electron volts l in nanometers for a photon ! Interference of larger particles   Matter-wave interference has now been demonstrated with electrons, neutrons, atoms, small molecules, BIG molecules, & biological molecules Recent Example: Interference of C60, a.k.a “fullerenes”, “buckyballs” Mass = (60 C)(12 g/mole) = 1.2 x 10-24 kg p2  K E  kT 2m  p  3kTm  2.11022 kg m / s l = h/p = 2.9 pm (c.f C60 is ~ nm across!) [A Zeilinger (U Vienna), 1999] ... Lecture 6: Introduction to Quantum Physics: Matter Waves and the Schrödinger Equation Content  Electron Diffraction  Matter- wave Interference   particles as waves  Composite... see later that the discrete atomic emission lines also arise from the wavelike properties of the electrons in the field of the nucleus: Atomic hydrogen I(q) Electrons can act like waves! ! 60 q... 8.8  106 eV Compared to the energy of the photon (given above): E  pc  3eV Wavelength of an Electron  The DeBroglie wavelength of an electron is inversely related to the electron momentum: