Lecture 2 Flashcards
Longer cavity of sound travel means
Lower sounds since
Resonant frequency decreased and wavelength increased
Till slide 10
Ask what is supposed to tell us
In making the wave equation what are the assumptions we use
That the wave does not change over time, it it’s resonating (time independent)
The wave starts at the boundary x=0
The wave is composed of sin and cos functions
What is the simplified wave equation before the boundary conditions
= C cos (kx) + D sin (kx)
What are the boundary conditions for the wave
At x=0 and L=0, wave function is zero
It can’t exist outside these boundary’s
Because of the boundary limit, what does the wave equation then become
= D sin (kx)
Because the C constants has to always equal zero to fulfil the boundary rule
What does the second boundary condition do the the wave equation
At x=L wave function is also zero so
D sin (kL) has to all equal zero at x=L
Only when kL= n(pi) is the whole thing zero
What can kL= n(pi) help us with in the wave equation
Can isolate for k
k=n(pi)/L
Then plug into wave equation
D sin (x n(pi)/L)
What is the lowest number that n can be in the wave equation and why
1 because that gives half a wave, any lower and it is not a wave anymore
What is a node
What is an antinode
Node is the n-1
Antinode is the n
Ex. If n=2 that’s a full wave that has one node and two antinodes
Slide 23
What about carbon bond is important
What is particle in a box
When the electron is more and more restricted/confined in a boundary, we see it as a wave instead of particle
What is the Schrödinger wave equation
H | ¥ = E |¥
This means the H of the wave function equals the E of the wave function
It’s the quantum interpretation of the matter wave
What is H and E in the schroedinger wave equation
H is the kinetic and potential energy
E is the observable energy
Learn how to make simplified version of shrodinger equation using the boundary conditions
Slide 30 and tut 2
Is relation to the Schrödinger equation, n=1 is
The ground state energy, can’t go lower
Where is the highest probability of finding the electron in its wave
Least
At the antinodes
At the nodes (not the boundary’s because this are not nodes)
How do you find energy levels of the piaB wave
Since E0 is when n=1 and there is half wave,
n=2 is E0(2^2) so E1= E0(4)
Then E0(3^2) so. E2= E0(9)
Slides 37 and 38
Ask for explain
What does Eg + Ec = E photon mean
The normal energy gap between levels plus the addition energy due to being confined makes up the energy of the releases photon
This means that electrons gain more energy (Ec) than normal from being trapped between boundary’s
Slide 39
Diff coloured things explain why