7. Angular momentum Flashcards
What parts of the solution to the 3D TISE form the spherical harmonics?
The angular parts of ϴ and Φ so they are functions of (ϴ,Φ)
What are the key points about the solution of ϴ?
- l should be a non -ve number
- there are polynomials in cos(ϴ)
- complex
- For the Coulomb 1/r potential, tthe max quantum number = n-1
What do we call the maximum quantum number and what is it equal to?
The principle quantum number, equal to n-1
State the symbols for the principal, orbital and magnetic quantum numbers
n - principal quantum number
l - orbital quantum number
m_l - magnetic quantum number
State the values for the principal, orbital and magnetic quantum numbers
n = 1,2,3,4... l = 0,1,2, ... n-1 m_l = -l, -l +1, ... l-1, l
State the magnitude for the angular momentum
|L| = mvr
Imagine that the angular momentum is parallel to the z axis. State the directions of its components
It is parallel to the z axis (up)
-> orbit is anti clockwise in the x-y plane (RH grip)
State the results of the theoretical situation when the angular momentum is parallel to z
v_z = 0, so Δv_z = 0 Δp_z = 0 Δz = infinity NOT ALLOWED BY HUP
How much of the angular momentum are we allowed to know?
The magnitude of |L| and one component - usually denoted L_z
State the equations of L_z and |L|
L_z = h_bar m_l |L| = h_bar sqrt( l (l+1) )
What was wrong with the old Bohr model of the atom?
- It described the quantisation of the angular momentum wrong ( |L| = n h_bar ). It describes the maximum angular momentum well for large quantum numbers but not for small ones
- It cannot describe a state with 0 |L|
State how the angular momentum is quantised and its quantum number
L is quantised with units of h_bar and has a quantum number of l
See page 3 of document for the components of the angular momentum
do it lmao
What can be said about the axis of the central potential?
It is isotropic - no preferred axis
Give an example of a pertubation for a central potential
A magnetic field
