Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Path integral formulation wikipedia, lookup

Particle in a box wikipedia, lookup

Ising model wikipedia, lookup

Renormalization wikipedia, lookup

Hidden variable theory wikipedia, lookup

Scalar field theory wikipedia, lookup

Schrödinger equation wikipedia, lookup

Magnetoreception wikipedia, lookup

Quantum electrodynamics wikipedia, lookup

Renormalization group wikipedia, lookup

Magnetic monopole wikipedia, lookup

Erwin Schrödinger wikipedia, lookup

Paul Dirac wikipedia, lookup

Bell's theorem wikipedia, lookup

Wave function wikipedia, lookup

Canonical quantization wikipedia, lookup

Nitrogen-vacancy center wikipedia, lookup

Atomic orbital wikipedia, lookup

T-symmetry wikipedia, lookup

Electron configuration wikipedia, lookup

Quantum state wikipedia, lookup

History of quantum field theory wikipedia, lookup

Electron paramagnetic resonance wikipedia, lookup

Aharonov–Bohm effect wikipedia, lookup

Atomic theory wikipedia, lookup

Bohr model wikipedia, lookup

Dirac equation wikipedia, lookup

Spin (physics) wikipedia, lookup

Theoretical and experimental justification for the Schrödinger equation wikipedia, lookup

Ferromagnetism wikipedia, lookup

Symmetry in quantum mechanics wikipedia, lookup

Relativistic quantum mechanics wikipedia, lookup

Hydrogen atom wikipedia, lookup

Transcript
```(normal)
Zeeman Effect with Spin
In strong external magnetic fields B, orbital and spin magnetic moments are both
coupled to B (and not to each other): In this case, z-components of the moments are
No magnetic field
With magnetic field, no spin
With magnetic field and spin
l=1, ml=+1, ms=+1/2
l=1, ml=0, ms=+1/2
l=1, ml=+1, ms=-1/2 and
l=1, ml=-1, ms=+1/2
l=1, ml=0, ms=-1/2
n=2, l=1
l=1, ml=-1, ms=-1/2
l=0, ml=0, ms=+1/2
n=1, l=0
l=0, ml=0, ms=-1/2
(note: no spin-orbit coupling in this diagram. We will later learn that some transitions are forbidden)
Spin-Orbit Interaction
In the absence of an external magnetic field (or a weak field), orbital and spin
magnetic moments interact.
From the perspective of the electron, the (positively
charged, Ze+) nucleus orbits around it. This creates a
magnetic moment at the site of the electron.
The electron energy is higher (less stable), if spin S is aligned with B.
The electron energy is lower (more stable), if spin S is aligned opposite to B.
When spin-orbit coupling is in effect, neither
L nor S are angular momentum conserved;
only the total angular momentum J=L+S is
conserved. This replaces the set of quantum
numbers
(l, ml, s, ms)
with a new set.
(l, s, j, mj)
l=2, s=1/2 ! j=5/2 and j=3/2
Total angular momentum vector:
l=2, j=5/2, mj=3/2
Quantum numbers:
Spectroscopic Notation (Term Symbols)
General Form:
l : orbital angular momentum quantum number.
s: spin quantum number.
j: total angular momentum quantum number.
2s+1 : “Spin Multiplicity” " total number of spin states
[e.g. 2s+1=2 (up and down) for s=1/2].
Example: hydrogen atom (lowest states):
(note: In this example, spin multiplicity is always 2 because hydrogen has only one electron.
Total angular momentum quantum number j is either l+1/2 or l-1/2).
Dirac Relativistic Hydrogen Atom
The Bohr/Schrödinger result for hydrogen
Bohr/Schrödinger
Dirac
is
based
on
non-relativistic
(Newtonian) mechanics.
The (special-) relativistic equivalent to
the Schrödinger equation is the Dirac
equation. The Dirac equation, naturally
explains spin (and spin-orbit coupling),
giving the following energy equation of
hydrogen.
(Fine structure constant)
Shift of Dirac levels relative to Bohr/Schrödinger is
exaggerated by a factor of (1/#2).
```
Related documents