Quantum continued wave functions

1
Quantum continued (wave functions)
PH103
Dr. James van Howe Lecture 20
May 5, 2008
Erwin Schrodinger- put the wave mechanics in
Quantum Mechanics
2
(No Transcript)
3
True or False
A particle of light has zero rest energy
4
True or False
Increasing the intensity of photons incident on a
metal surface increases the kinetic energy with
which electrons are ejected from the metal.
5
True or False
Knowing that Ehf, for black body radiation, as
frequency goes up indefinitely, so does the
intensity
6
The color of a photon that scatters off of an
electron (Compton scattering) becomes ______
compared to before scattering

• Bluer
• Redder
• Does not change color

7
As the momentum of a particle gets smaller, its
de Broglie wavelength becomes

• Larger
• Smaller
• Stays the same

8
Why dont we see matter waves (or at least the
effects of matter waves) in daily life?

• Typical objects are too big and so the de Broglie
  wavelength is too big
• Typical objects are too big and and so the de
  Broglie wavelength is too small
• Typical objects are too small and so the de
  Broglie wavelength is too big
• Typical objects are too small and and so the de
  Broglie wavelength is too small

9
True or False
In a quantized system, if the wave function of a
particle is zero at a position, then there is
zero probability of observing the particle at
that position
10
Names______________________________________
PH103, de Broglie Waves
1. Calculate the de Broglie wavelength for the
following a) A 142 gram baseball thrown at 90
mph (40 m/s). Recall h6.626x10-34 Js b) An
electron is given a kinetic energy of 10 keV
(since KE is smaller than the rest mass, use the
non-relativistic equation for kinetic energy).
Note h4.135x10-15 eV s and hc1240 eVnm,
me0.511 MeV/c2 Note Trick that can make
calc. easier c) Looking at the equation for de
Broglie wavelength and the previous examples,
when is the wavelength (and therefore wave-nature
of matter) noticeable? 2. For many electrons
like those in 1 b), At what distance from the
central max would you find the third diffraction
maximum after they are sent through a double
slit. Here the slit spacing is 0.05 nm apart and
the distance to the screen is 10 m?
11
Names______________________________________
PH103, De Broglie Waves
1. Calculate the de Broglie wavelength for the
following a) A 142 gram baseball thrown at 90
mph (40 m/s). Recall h6.626x10-34 Js b) An
electron is given a kinetic energy of 10 keV
(since KE is smaller than the rest mass, use the
non-relativistic equation for kinetic energy).
Note h4.135x10-15 eV s and hc1240 eVnm,
me0.511 MeV/c2 Note Trick that can make
calc. easier c) Looking at the equation for de
Broglie wavelength and the previous examples,
when is the wavelength (and therefore wave nature
of matter) noticeable? The de Broglie wavelength
is only noticeable when the momentum mv is small
plth. This happens the most for extremely small
masses like atoms. Bigger stuff just doesnt work
and why we are not use to seeing matter waves in
daily life. 2. For many electrons like those in
1 b), At what distance from the central max would
you find the third diffraction maximum after they
are sent through a double slit. Here the slit
spacing is 0.05 nm apart and the distance to the
screen is 10 m?
12
We calculated wavelength for photons and matter
but what do the waves mean?
13
Schrodinger Equation
Wave mechanics (quantum mechanics) was born when
Erwin Schrodinger introduced the following
equation in 1926 to describe the wave-like nature
of particles
14
The Wavefunction is related to probability of
observing the particle
15
Simplest Wavefunction Free Particle
Free particle means no potential Energy
O.k. this may look scary and nasty, but youve
seen it before. Its a sheep in wolves clothing!
Same form as a mass on a spring! Simple harmonic
oscillator!
In fact, almost everything in physics is really
just a simple harmonic oscillator or combinations
of SHOs
16
Simplest Wavefunction Free Particle
This is great because we can apply everything we
know about SHO (simple harmonic oscillator) and
waves to QM (quantum mechanics)!
k
m
m
Allowed Energy (not quantized so cant really
talk about probability here)
17
Next Simplest Particle in a box
Inside is just like the free particle, no
potential
Walls are like an infinitely steep hill- no way
the particle can escape
m
We want to know two things 1) The allowed
energy states of the particle 2) The probability
of finding the particle at a spot, given an
energy state
18
Inside is just like the free particle, no
potential
Walls are like an infinitely steep hill- no way
the particle can escape
m
From Schrodingers Equation we find
19
Names______________________________________
PH103, Particle in a box
1. Draw the first three modes (n1,2,3) for this
wave function. Think standing waves on a string
with fixed ends. Because the ends are fixed
(infinite potential) you must have nodes at the
ends. 2. Inside the box the
energy is just like the free particle and so we
can use the relation between energy and
wavelength Using the wave function given in
part 1 (information inside the sine wave), plug
in the correct expression for l to get energy in
terms of n and L.