1. Quantum Mechanics

2. History
Beginning in 1900, some experiments showed some disagreement with “classical” mechanics and understanding of light
Planck/Einstein first people to propose a key idea
Light was made up of particles = photons

3. Quantum Quanta – Latin for little bits
Light is quantized = comes in little bits/particles
Light acts like a wave (interference)
Light acts like a particle (photoelectric effect)

4. Photoelectric effect Einstein – 1905 – Nobel Prize
Light comes in and hits a metal
Electrons leave the metal with a given energy
Explanation: Photons have a collision with electrons and transfer energy/momentum to the electron
Data matched theory exceptionally well

5. Light Light has energy/momentum E = hf = hc/l p = E/c = h/l
h = Planck’s constant = x 10-34

6. Particle-Wave Duality
If a wave (like light) acts like a particle, can particles act like waves?

7. Electrons as waves
Previous pattern means that electrons interfere with each other
They act like waves
What is their wavelength?
Pattern consistent with a wavelength
l = h/p
Same relation as with light
Called the deBroglie wavelength

8. Now what?
If electrons (and other particles) can act like waves, what else can they do?
They can setup standing waves
Waves with particular wavelength/frequency that appear to not be travelling

9. Electron standing waves
Electrons in a box (like strings fixed at both ends) have a standing wave pattern
Different harmonics have different frequencies
Difference frequencies means different energies

10. Standing waves Recall: E = ½ mv2 and p = mv  E = p2/2m
p = h/l and l = 2L/n
Put it all together: E = n2h2/(8mL2)
Only certain energies are allowed (n=1,2,3,…)
Energy is quantized

11. Electrons in an atom
Electrons can form standing waves going around a nucleus
Only some wavelengths fit  only certain energy levels
nl = 2pr

12. Energy levels E = ½ mv2 = h2/(2ml2)
Use l = 2pr/n and r = a0 = Bohr radius
E = n2h2/(8p2ma02)
Theory: Use n = 1 and a0 = 5.29 x m
E1 = 2.18 x J
Measured value: x J

13. Particles as Waves
If particles can be described by waves, they are constantly moving
Location can be described by a wave function
Amplitude of wave given by Y(x,t)
Probability of being at a certain place is given by Y2(x,t)
Theory of quantum mechanics is essentially an equation telling you how to find this wavefunction

14. Schrodinger Equation
Describes where a particle is as a function of time
Here it is:
Solution is the wavefunction!
Only certain solutions allowed for particular values of E  Energy is quantized

15. Schrodinger Equation
Can use this to solve the electron in the box and the Hydrogen atom
Gives the solutions that we had before for the energies
What does the wavefunction look like?
Where is the electron?

16. Hydrogen atom
A few solutions for the Hydrogen atom
Look familiar?

17. Atomic orbitals

18. Electron orbitals
The shape of the electron orbitals is given by the solution to the Schrodinger equation
Remember: all came about because energy is quantized because electrons act like (standing) waves

19. Quantum Mechanics

20. Other Quantum Weirdness
Heisenberg Uncertainty principle
Can’t measure the position and the velocity/momentum at the same
Meaning: The act of measuring the location an object affects its momentum, so can’t know both at the same time

21. Probability Everything described by a wavefunction
Tells you probability of where something is  can’t tell you for certain
Has some probability that a particle is here and there at the same time
Won’t know until you measure it

22. Schrodinger’s Cat
Put cat in box with a radioactive compound that has some probability of decaying and close the box
Cat has some probability that it dies and some probability that it lives
We say that cat is in a superposition of dead and alive states
Won’t know until we open the box

23. Tunneling Look at the p orbital Probability that electron in top half
Probability that electron in bottom half
Node in the middle – no probability
So particle can travel from the top part to the bottom part without going through the middle  tunneling