PHYS 30101 Quantum Mechanics

1
PHYS 30101 Quantum Mechanics
Lecture 19
Dr Jon Billowes Nuclear Physics Group (Schuster
Building, room 4.10) j.billowes_at_manchester.ac.uk
These slides at http//nuclear.ph.man.ac.uk/jb/p
hys30101
2

• Syllabus
• Basics of quantum mechanics (QM) Postulate,
  operators, eigenvalues eigenfunctions,
  orthogonality completeness, time-dependent
  Schrödinger equation, probabilistic
  interpretation, compatibility of observables,
  the uncertainty principle.
• 1-D QM Bound states, potential barriers,
  tunnelling phenomena.
• Orbital angular momentum Commutation relations,
  eigenvalues of Lz and L2, explicit forms of Lz
  and L2 in spherical polar coordinates, spherical
  harmonics Yl,m.
• Spin Noncommutativity of spin operators, ladder
  operators, Dirac notation, Pauli spin matrices,
  the Stern-Gerlach experiment.
• Addition of angular momentum Total angular
  momentum operators, eigenvalues and
  eigenfunctions of Jz and J2.
• The hydrogen atom revisited Spin-orbit coupling,
  fine structure, Zeeman effect.
• Perturbation theory First-order perturbation
  theory for energy levels.
• Conceptual problems The EPR paradox, Bells
  inequalities.

3
Plan Include coupling of orbital and spin
angular momenta in Hamiltonian for hydrogen atom
S
L
4
6. The hydrogen atom revisited - Reminder of
eigenfunctions, eigenvalues and quantum numbers
n, l, ml of hydrogen atom. 6.1 Spin-orbit
coupling and the fine structure. 6.2 Zeeman
effect for single electron atoms in (a) a
weak magnetic field (b) a strong
magnetic field 6.3 Spin in magnetic field QM
and classical descriptions
5
Recap Brief reminder of QM description of
hydrogen atom
TISE V(r) -e2/4p eo r
Remember
Angular part written
Solve by separation of variables To get radial
equation
6
Eigenenergies En E1/n2 where E1 -13.6
eV
n 1, 2, 3, 4.
Allowed values of l l 0, 1, 2, 3 ,
(n-1).
Allowed values of lz ml l, l-1, l-2,., 0,
-1, , -l
(2l 1 values)