Weird experiments Schrödinger equation

centrifugal is Latin for Bohr model of an atom 1913 centrifugal is Latin for "center fleeing" It does not exist! http://regentsprep.org/Regents/physics/phys06/bcentrif/centrif.htm

Bohr model of an atom 1913 Potential energy of the electron “Introduction to wave phenomena” by Akira Hirose and Karl Lonngren

Bohr model of an atom 1913 Kinetic energy of the electron Total energy of the electron electron angular momentum

Bohr model of an atom 1913 electron angular momentum Niels Bohr postulated that the momentum was quantized h is Planck’s constant 6.626068 × 10-34 m2 kg / s The radius is found to be

Bohr model of an atom 1913 The energy then becomes quantized http://csep10.phys.utk.edu/astr162/lect/light/bohr.html

Photo electric effect - Einstein Energy of a photon E = h http://regentsprep.org/Regents/physics/phys05/catomodel/bohr.htmHoudon

Einstein’s explanation

Bohr model of an atom 1913 What is the frequency of the light that will be emitted by an electron as it moves from the n = 2 down to n = 1? Ionization implies n → 

Experiment to understand the photo electric effect.

Experimental conclusions The frequency must be greater than a “cut off frequency” that changes with different metals. Kinetic energy of the emitted electrons depends upon the frequency of the incident light. Kinetic energy of the electrons is independent of the intensity of the incident light.

Sodium has a work function of W = 1.8 eV. Find the cutoff frequency. red

A metal with a work function of 2 A metal with a work function of 2.3 eV is illuminated with ultraviolet radiation l = 3000 Ǻ. Calculate the energy of the photo electrons that are emitted from the surface.

Current Voltage http://hyperphysics.phy-astr.gsu.edu/hbase/FrHz.html Franck-Hertz experiment in mercury vapor. Electrons are accelerated and the current is monitored. 1914 (In 1887, Hertz noted that electrons would be emitted from a metal that was illuminated with light.) Current Voltage http://hyperphysics.phy-astr.gsu.edu/hbase/FrHz.html

Reflected wave is strong if n = 2d sin

Davisson-Germer experiment – electrons incident on nickel 1925 http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html

Interpretation of the Davisson-Germer experiment Energy of a photon E = h Waves Particles

de Broglie wavelength de Broglie argued that there was a wavelength that could be written from

Interpretation of the Davisson-Germer experiment Conclusion Waves & particles have many similarities!

Schrödinger equation

Schrödinger equation

Schrödinger equation A wave can be written as Operator One dimension Three dimensions

Schrödinger equation What is the meaning?

Schrödinger equation a0 +2 -2 1 a1 a0 a2 a1 a0 a2 a1 a0 a2 a1 a0 a2

Solving the one-dimensional Schrödinger equation.

Schrödinger equation electron in free space

Schrödinger equation - E - E

Infinite potential well Schrödinger equation Infinite potential well

Schrödinger equation Three-dimensional Laplacian operator in Cartesian coordinates Separation of variables Three ordinary differential equations plus one algebraic equation

Schrödinger equation Pauli exclusion principle 2 electrons cannot have the same quantum numbers. Electron spin => +1/2 & -1/2 Schrödinger equation Integers called quantum numbers One particular boundary condition Algebraic equation

Schrödinger equation

Schrödinger equation Atoms approximately are three-dimensional spherical objects. Electron spin => +1/2 & -1/2 Trigonometric function Bessel function Legendre polynomial

Schrödinger equation Bessel function Legendre polynomial One can satisfy different boundary conditions. This leads to certain integers. Quantum numbers. Pauli exclusion principle 2 electrons cannot have the same quantum numbers.

shell is filled! Schrödinger equation Pauli exclusion principle 2 electrons cannot have the same quantum numbers. element n l m s Hydrogen 1 +1/2 or -1/2 Helium 1 +1/2 & -1/2 Lithium 2 +1/2 or -1/2 shell is filled! Beryllium 2 +1/2 & -1/2

Heisenberg uncertainty principle Particle slows down - conservation of energy - photo electric effect Deviation must be greater than the wavelength http://www.aip.org/history/heisenberg/