1. Weird experiments
Schrödinger equation

2. centrifugal is Latin for
Bohr model of an atom 1913
centrifugal is Latin for
"center fleeing"
It does not exist!

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

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

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

6. Bohr model of an atom 1913 The energy then becomes quantized

7. Photo electric effect - Einstein
Energy of a photon E = h

8. Einstein’s explanation

9. 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 → 

10. Experiment to understand the photo electric effect.

11. 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.

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

13. 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.

14. 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 (In 1887, Hertz noted that electrons would be emitted from a metal that was illuminated with light.)
Current
Voltage

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

16. Davisson-Germer experiment – electrons incident on nickel

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

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

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

20. Schrödinger equation

21. Schrödinger equation

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

23. Schrödinger equation
What is the meaning?

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

25. Solving the one-dimensional Schrödinger equation.

26. Schrödinger equation electron in free space

27. Schrödinger equation
- E
- E

28. Infinite potential well
Schrödinger equation
Infinite potential well

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

30. 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

31. Schrödinger equation

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

33. 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.

34. 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

35. Heisenberg uncertainty principle
Particle slows down - conservation of energy - photo electric effect
Deviation must be greater than the wavelength